text: // math_fwd.hpp
  
  // TODO revise completely for new distribution classes.
  
  // Copyright Paul A. Bristow 2006.
  // Copyright John Maddock 2006.
  
  // Use, modification and distribution are subject to the
  // Boost Software License, Version 1.0.
  // (See accompanying file LICENSE_1_0.txt
  // or copy at http://www.boost.org/LICENSE_1_0.txt)
  
  // Omnibus list of forward declarations of math special functions.
  
  // IT = Integer type.
  // RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types
  // AT = Integer or Real type
  
  #ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP
  #define BOOST_MATH_SPECIAL_MATH_FWD_HPP
  
  #ifdef _MSC_VER
  #pragma once
  #endif
  
  #include <boost/math/special_functions/detail/round_fwd.hpp>
  #include <boost/math/tools/promotion.hpp> // for argument promotion.
  #include <boost/math/policies/policy.hpp>
  #include <boost/mpl/comparison.hpp>
  #include <boost/utility/enable_if.hpp>
  #include <boost/config/no_tr1/complex.hpp>
  
  #define BOOST_NO_MACRO_EXPAND /**/
  
  namespace boost
  {
     namespace math
     { // Math functions (in roughly alphabetic order).
  
     // Beta functions.
     template <class RT1, class RT2>
     typename tools::promote_args<RT1, RT2>::type
           beta(RT1 a, RT2 b); // Beta function (2 arguments).
  
     template <class RT1, class RT2, class A>
     typename tools::promote_args<RT1, RT2, A>::type
           beta(RT1 a, RT2 b, A x); // Beta function (3 arguments).
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments).
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           betac(RT1 a, RT2 b, RT3 x);
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           betac(RT1 a, RT2 b, RT3 x, const Policy& pol);
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function.
  
     template <class T1, class T2, class T3, class T4>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ibeta_inv(T1 a, T2 b, T3 p, T4* py);
  
     template <class T1, class T2, class T3, class T4, class Policy>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol);
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
  
     template <class T1, class T2, class T3, class T4>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ibetac_inv(T1 a, T2 b, T3 q, T4* py);
  
     template <class T1, class T2, class T3, class T4, class Policy>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol);
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
  
     template <class RT1, class RT2, class RT3>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_derivative(RT1 a, RT2 b, RT3 x);  // derivative of incomplete beta
  
     template <class RT1, class RT2, class RT3, class Policy>
     typename tools::promote_args<RT1, RT2, RT3>::type
           ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol);  // derivative of incomplete beta
  
     // Binomial:
     template <class T, class Policy>
     T binomial_coefficient(unsigned n, unsigned k, const Policy& pol);
     template <class T>
     T binomial_coefficient(unsigned n, unsigned k);
  
     // erf & erfc error functions.
     template <class RT> // Error function.
     typename tools::promote_args<RT>::type erf(RT z);
     template <class RT, class Policy> // Error function.
     typename tools::promote_args<RT>::type erf(RT z, const Policy&);
  
     template <class RT>// Error function complement.
     typename tools::promote_args<RT>::type erfc(RT z);
     template <class RT, class Policy>// Error function complement.
     typename tools::promote_args<RT>::type erfc(RT z, const Policy&);
  
     template <class RT>// Error function inverse.
     typename tools::promote_args<RT>::type erf_inv(RT z);
     template <class RT, class Policy>// Error function inverse.
     typename tools::promote_args<RT>::type erf_inv(RT z, const Policy& pol);
  
     template <class RT>// Error function complement inverse.
     typename tools::promote_args<RT>::type erfc_inv(RT z);
     template <class RT, class Policy>// Error function complement inverse.
     typename tools::promote_args<RT>::type erfc_inv(RT z, const Policy& pol);
  
     // Polynomials:
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
           legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);
  
     template <class T>
     typename tools::promote_args<T>::type
           legendre_p(int l, T x);
  #if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
     template <class T, class Policy>
     typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
           legendre_p(int l, T x, const Policy& pol);
  #endif
     template <class T>
     typename tools::promote_args<T>::type
           legendre_q(unsigned l, T x);
  #if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
     template <class T, class Policy>
     typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
           legendre_q(unsigned l, T x, const Policy& pol);
  #endif
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
           legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1);
  
     template <class T>
     typename tools::promote_args<T>::type
           legendre_p(int l, int m, T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type
           legendre_p(int l, int m, T x, const Policy& pol);
  
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
           laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1);
  
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
        laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1);
  
     template <class T>
     typename tools::promote_args<T>::type
        laguerre(unsigned n, T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type
        laguerre(unsigned n, unsigned m, T x, const Policy& pol);
  
     template <class T1, class T2>
     struct laguerre_result
     {
        typedef typename mpl::if_<
           policies::is_policy<T2>,
           typename tools::promote_args<T1>::type,
           typename tools::promote_args<T2>::type
        >::type type;
     };
  
     template <class T1, class T2>
     typename laguerre_result<T1, T2>::type
        laguerre(unsigned n, T1 m, T2 x);
  
     template <class T>
     typename tools::promote_args<T>::type
        hermite(unsigned n, T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type
        hermite(unsigned n, T x, const Policy& pol);
  
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
        hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1);
  
     template <class T1, class T2>
     std::complex<typename tools::promote_args<T1, T2>::type>
           spherical_harmonic(unsigned n, int m, T1 theta, T2 phi);
  
     template <class T1, class T2, class Policy>
     std::complex<typename tools::promote_args<T1, T2>::type>
        spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type
           spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type
        spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type
           spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type
        spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
  
     // Elliptic integrals:
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
           ellint_rf(T1 x, T2 y, T3 z);
  
     template <class T1, class T2, class T3, class Policy>
     typename tools::promote_args<T1, T2, T3>::type
           ellint_rf(T1 x, T2 y, T3 z, const Policy& pol);
  
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
           ellint_rd(T1 x, T2 y, T3 z);
  
     template <class T1, class T2, class T3, class Policy>
     typename tools::promote_args<T1, T2, T3>::type
           ellint_rd(T1 x, T2 y, T3 z, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type
           ellint_rc(T1 x, T2 y);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type
           ellint_rc(T1 x, T2 y, const Policy& pol);
  
     template <class T1, class T2, class T3, class T4>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ellint_rj(T1 x, T2 y, T3 z, T4 p);
  
     template <class T1, class T2, class T3, class T4, class Policy>
     typename tools::promote_args<T1, T2, T3, T4>::type
           ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol);
  
     template <class T1, class T2, class T3>
     typename tools::promote_args<T1, T2, T3>::type
        ellint_rg(T1 x, T2 y, T3 z);
  
     template <class T1, class T2, class T3, class Policy>
     typename tools::promote_args<T1, T2, T3>::type
        ellint_rg(T1 x, T2 y, T3 z, const Policy& pol);
  
     template <typename T>
     typename tools::promote_args<T>::type ellint_2(T k);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi, const Policy& pol);
  
     template <typename T>
     typename tools::promote_args<T>::type ellint_1(T k);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol);
  
     template <typename T>
     typename tools::promote_args<T>::type ellint_d(T k);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol);
  
     namespace detail{
  
     template <class T, class U, class V>
     struct ellint_3_result
     {
        typedef typename mpl::if_<
           policies::is_policy<V>,
           typename tools::promote_args<T, U>::type,
           typename tools::promote_args<T, U, V>::type
        >::type type;
     };
  
     } // namespace detail
  
  
     template <class T1, class T2, class T3>
     typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi);
  
     template <class T1, class T2, class T3, class Policy>
     typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v);
  
     // Factorial functions.
     // Note: not for integral types, at present.
     template <class RT>
     struct max_factorial;
     template <class RT>
     RT factorial(unsigned int);
     template <class RT, class Policy>
     RT factorial(unsigned int, const Policy& pol);
     template <class RT>
     RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT));
     template <class RT>
     RT double_factorial(unsigned i);
     template <class RT, class Policy>
     RT double_factorial(unsigned i, const Policy& pol);
  
     template <class RT>
     typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol);
  
     template <class RT>
     typename tools::promote_args<RT>::type rising_factorial(RT x, int n);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol);
  
     // Gamma functions.
     template <class RT>
     typename tools::promote_args<RT>::type tgamma(RT z);
  
     template <class RT>
     typename tools::promote_args<RT>::type tgamma1pm1(RT z);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol);
  
     template <class RT1, class RT2>
     typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z);
  
     template <class RT1, class RT2, class Policy>
     typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol);
  
     template <class RT>
     typename tools::promote_args<RT>::type lgamma(RT z, int* sign);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol);
  
     template <class RT>
     typename tools::promote_args<RT>::type lgamma(RT x);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol);
  
     template <class RT1, class RT2>
     typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z);
  
     template <class RT1, class RT2, class Policy>
     typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&);
  
     template <class RT1, class RT2>
     typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z);
  
     template <class RT1, class RT2, class Policy>
     typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&);
  
     template <class RT1, class RT2>
     typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z);
  
     template <class RT1, class RT2, class Policy>
     typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&);
  
     // gamma inverse.
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&);
  
     // digamma:
     template <class T>
     typename tools::promote_args<T>::type digamma(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type digamma(T x, const Policy&);
  
     // trigamma:
     template <class T>
     typename tools::promote_args<T>::type trigamma(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type trigamma(T x, const Policy&);
  
     // polygamma:
     template <class T>
     typename tools::promote_args<T>::type polygamma(int n, T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type polygamma(int n, T x, const Policy&);
  
     // Hypotenuse function sqrt(x ^ 2 + y ^ 2).
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type
           hypot(T1 x, T2 y);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type
           hypot(T1 x, T2 y, const Policy&);
  
     // cbrt - cube root.
     template <class RT>
     typename tools::promote_args<RT>::type cbrt(RT z);
  
     template <class RT, class Policy>
     typename tools::promote_args<RT>::type cbrt(RT z, const Policy&);
  
     // log1p is log(x + 1)
     template <class T>
     typename tools::promote_args<T>::type log1p(T);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type log1p(T, const Policy&);
  
     // log1pmx is log(x + 1) - x
     template <class T>
     typename tools::promote_args<T>::type log1pmx(T);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type log1pmx(T, const Policy&);
  
     // Exp (x) minus 1 functions.
     template <class T>
     typename tools::promote_args<T>::type expm1(T);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type expm1(T, const Policy&);
  
     // Power - 1
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type
           powm1(const T1 a, const T2 z);
  
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type
           powm1(const T1 a, const T2 z, const Policy&);
  
     // sqrt(1+x) - 1
     template <class T>
     typename tools::promote_args<T>::type sqrt1pm1(const T& val);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&);
  
     // sinus cardinals:
     template <class T>
     typename tools::promote_args<T>::type sinc_pi(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type sinc_pi(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type sinhc_pi(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&);
  
     // inverse hyperbolics:
     template<typename T>
     typename tools::promote_args<T>::type asinh(T x);
  
     template<typename T, class Policy>
     typename tools::promote_args<T>::type asinh(T x, const Policy&);
  
     template<typename T>
     typename tools::promote_args<T>::type acosh(T x);
  
     template<typename T, class Policy>
     typename tools::promote_args<T>::type acosh(T x, const Policy&);
  
     template<typename T>
     typename tools::promote_args<T>::type atanh(T x);
  
     template<typename T, class Policy>
     typename tools::promote_args<T>::type atanh(T x, const Policy&);
  
     namespace detail{
  
        typedef mpl::int_<0> bessel_no_int_tag;      // No integer optimisation possible.
        typedef mpl::int_<1> bessel_maybe_int_tag;   // Maybe integer optimisation.
        typedef mpl::int_<2> bessel_int_tag;         // Definite integer optimistaion.
  
        template <class T1, class T2, class Policy>
        struct bessel_traits
        {
           typedef typename mpl::if_<
              is_integral<T1>,
              typename tools::promote_args<T2>::type,
              typename tools::promote_args<T1, T2>::type
           >::type result_type;
  
           typedef typename policies::precision<result_type, Policy>::type precision_type;
  
           typedef typename mpl::if_<
              mpl::or_<
                 mpl::less_equal<precision_type, mpl::int_<0> >,
                 mpl::greater<precision_type, mpl::int_<64> > >,
              bessel_no_int_tag,
              typename mpl::if_<
                 is_integral<T1>,
                 bessel_int_tag,
                 bessel_maybe_int_tag
              >::type
           >::type optimisation_tag;
           typedef typename mpl::if_<
              mpl::or_<
                 mpl::less_equal<precision_type, mpl::int_<0> >,
                 mpl::greater<precision_type, mpl::int_<113> > >,
              bessel_no_int_tag,
              typename mpl::if_<
                 is_integral<T1>,
                 bessel_int_tag,
                 bessel_maybe_int_tag
              >::type
           >::type optimisation_tag128;
        };
     } // detail
  
     // Bessel functions:
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol);
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x);
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x);
  
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol);
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol);
  
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x);
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x);
  
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol);
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x);
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x);
  
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol);
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x);
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x);
  
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol);
     template <class T1, class T2, class Policy>
     typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x);
     template <class T1, class T2>
     typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x);
  
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol);
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol);
  
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x);
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x);
  
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol);
  
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m);
  
     template <class T, class OutputIterator>
     OutputIterator cyl_bessel_j_zero(T v,
                            int start_index,
                            unsigned number_of_zeros,
                            OutputIterator out_it);
  
     template <class T, class OutputIterator, class Policy>
     OutputIterator cyl_bessel_j_zero(T v,
                            int start_index,
                            unsigned number_of_zeros,
                            OutputIterator out_it,
                            const Policy&);
  
     template <class T, class Policy>
     typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol);
  
     template <class T>
     typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m);
  
     template <class T, class OutputIterator>
     OutputIterator cyl_neumann_zero(T v,
                           int start_index,
                           unsigned number_of_zeros,
                           OutputIterator out_it);
  
     template <class T, class OutputIterator, class Policy>
     OutputIterator cyl_neumann_zero(T v,
                           int start_index,
                           unsigned number_of_zeros,
                           OutputIterator out_it,
                           const Policy&);
  
     template <class T1, class T2>
     std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x);
  
     template <class T1, class T2, class Policy>
     std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2, class Policy>
     std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x);
  
     template <class T1, class T2, class Policy>
     std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x);
  
     template <class T1, class T2, class Policy>
     std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol);
  
     template <class T1, class T2>
     std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type airy_ai(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type airy_ai(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type airy_bi(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type airy_bi(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type airy_ai_prime(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type airy_ai_prime(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type airy_bi_prime(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type airy_bi_prime(T x);
  
     template <class T>
     T airy_ai_zero(int m);
     template <class T, class Policy>
     T airy_ai_zero(int m, const Policy&);
  
     template <class OutputIterator>
     OutputIterator airy_ai_zero(
                       int start_index,
                       unsigned number_of_zeros,
                       OutputIterator out_it);
     template <class OutputIterator, class Policy>
     OutputIterator airy_ai_zero(
                       int start_index,
                       unsigned number_of_zeros,
                       OutputIterator out_it,
                       const Policy&);
  
     template <class T>
     T airy_bi_zero(int m);
     template <class T, class Policy>
     T airy_bi_zero(int m, const Policy&);
  
     template <class OutputIterator>
     OutputIterator airy_bi_zero(
                       int start_index,
                       unsigned number_of_zeros,
                       OutputIterator out_it);
     template <class OutputIterator, class Policy>
     OutputIterator airy_bi_zero(
                       int start_index,
                       unsigned number_of_zeros,
                       OutputIterator out_it,
                       const Policy&);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type sin_pi(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type sin_pi(T x);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type cos_pi(T x, const Policy&);
  
     template <class T>
     typename tools::promote_args<T>::type cos_pi(T x);
  
     template <class T>
     int fpclassify BOOST_NO_MACRO_EXPAND(T t);
  
     template <class T>
     bool isfinite BOOST_NO_MACRO_EXPAND(T z);
  
     template <class T>
     bool isinf BOOST_NO_MACRO_EXPAND(T t);
  
     template <class T>
     bool isnan BOOST_NO_MACRO_EXPAND(T t);
  
     template <class T>
     bool isnormal BOOST_NO_MACRO_EXPAND(T t);
  
     template<class T>
     int signbit BOOST_NO_MACRO_EXPAND(T x);
  
     template <class T>
     int sign BOOST_NO_MACRO_EXPAND(const T& z);
  
     template <class T, class U>
     typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y);
  
     template <class T>
     typename tools::promote_args_permissive<T>::type changesign BOOST_NO_MACRO_EXPAND(const T& z);
  
     // Exponential integrals:
     namespace detail{
  
     template <class T, class U>
     struct expint_result
     {
        typedef typename mpl::if_<
           policies::is_policy<U>,
           typename tools::promote_args<T>::type,
           typename tools::promote_args<U>::type
        >::type type;
     };
  
     } // namespace detail
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type expint(unsigned n, T z, const Policy&);
  
     template <class T, class U>
     typename detail::expint_result<T, U>::type expint(T const z, U const u);
  
     template <class T>
     typename tools::promote_args<T>::type expint(T z);
  
     // Zeta:
     template <class T, class Policy>
     typename tools::promote_args<T>::type zeta(T s, const Policy&);
  
     // Owen's T function:
     template <class T1, class T2, class Policy>
     typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a, const Policy& pol);
  
     template <class T1, class T2>
     typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a);
  
     // Jacobi Functions:
     template <class T, class U, class V, class Policy>
     typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&);
  
     template <class T, class U, class V>
     typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0);
  
     template <class U, class T, class Policy>
     typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta, const Policy& pol);
  
     template <class U, class T>
     typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta);
  
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta, const Policy& pol);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta);
  
  
     template <class T>
     typename tools::promote_args<T>::type zeta(T s);
  
     // pow:
     template <int N, typename T, class Policy>
     typename tools::promote_args<T>::type pow(T base, const Policy& policy);
  
     template <int N, typename T>
     typename tools::promote_args<T>::type pow(T base);
  
     // next:
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type nextafter(const T&, const U&, const Policy&);
     template <class T, class U>
     typename tools::promote_args<T, U>::type nextafter(const T&, const U&);
     template <class T, class Policy>
     typename tools::promote_args<T>::type float_next(const T&, const Policy&);
     template <class T>
     typename tools::promote_args<T>::type float_next(const T&);
     template <class T, class Policy>
     typename tools::promote_args<T>::type float_prior(const T&, const Policy&);
     template <class T>
     typename tools::promote_args<T>::type float_prior(const T&);
     template <class T, class U, class Policy>
     typename tools::promote_args<T, U>::type float_distance(const T&, const U&, const Policy&);
     template <class T, class U>
     typename tools::promote_args<T, U>::type float_distance(const T&, const U&);
     template <class T, class Policy>
     typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol);
     template <class T>
     typename tools::promote_args<T>::type float_advance(const T& val, int distance);
  
     template <class T, class Policy>
     typename tools::promote_args<T>::type ulp(const T& val, const Policy& pol);
     template <class T>
     typename tools::promote_args<T>::type ulp(const T& val);
  
     template <class T, class U>
     typename tools::promote_args<T, U>::type relative_difference(const T&, const U&);
     template <class T, class U>
     typename tools::promote_args<T, U>::type epsilon_difference(const T&, const U&);
  
     template<class T>
     T unchecked_bernoulli_b2n(const std::size_t n);
     template <class T, class Policy>
     T bernoulli_b2n(const int i, const Policy &pol);
     template <class T>
     T bernoulli_b2n(const int i);
     template <class T, class OutputIterator, class Policy>
     OutputIterator bernoulli_b2n(const int start_index,
                                         const unsigned number_of_bernoullis_b2n,
                                         OutputIterator out_it,
                                         const Policy& pol);
     template <class T, class OutputIterator>
     OutputIterator bernoulli_b2n(const int start_index,
                                         const unsigned number_of_bernoullis_b2n,
                                         OutputIterator out_it);
     template <class T, class Policy>
     T tangent_t2n(const int i, const Policy &pol);
     template <class T>
     T tangent_t2n(const int i);
     template <class T, class OutputIterator, class Policy>
     OutputIterator tangent_t2n(const int start_index,
                                         const unsigned number_of_bernoullis_b2n,
                                         OutputIterator out_it,
                                         const Policy& pol);
     template <class T, class OutputIterator>
     OutputIterator tangent_t2n(const int start_index,
                                         const unsigned number_of_bernoullis_b2n,
                                         OutputIterator out_it);
  
      } // namespace math
  } // namespace boost
  
  #ifdef BOOST_HAS_LONG_LONG
  #define BOOST_MATH_DETAIL_LL_FUNC(Policy)\
     \
     template <class T>\
     inline T modf(const T& v, boost::long_long_type* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
     \
     template <class T>\
     inline boost::long_long_type lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\
     \
     template <class T>\
     inline boost::long_long_type llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\
  
  #else
  #define BOOST_MATH_DETAIL_LL_FUNC(Policy)
  #endif
  
  #define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\
     \
     BOOST_MATH_DETAIL_LL_FUNC(Policy)\
     \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type \
     beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\
  \
     template <class RT1, class RT2, class A>\
     inline typename boost::math::tools::promote_args<RT1, RT2, A>::type \
     beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\
  \
     template <class T1, class T2, class T3, class T4>\
     inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type  \
     ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\
  \
     template <class T1, class T2, class T3, class T4>\
     inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
     ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
     ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
     ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\
  \
     template <class RT1, class RT2, class RT3>\
     inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
     ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\
  \
     template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\
  \
     using boost::math::legendre_next;\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type \
     legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type \
     legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\
  \
     using ::boost::math::legendre_next;\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type \
     legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\
  \
     using ::boost::math::laguerre_next;\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type \
     laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::laguerre_result<T1, T2>::type \
     laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type \
     hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\
  \
     using boost::math::hermite_next;\
  \
     template <class T1, class T2>\
     inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \
     spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
     spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
     spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\
  \
     template <class T1, class T2, class Policy>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
        spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
     ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
     ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
     ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\
  \
     template <class T1, class T2, class T3, class T4>\
     inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
     ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
     ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\
     \
     template <typename T>\
     inline typename boost::math::tools::promote_args<T>::type ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\
  \
     template <typename T>\
     inline typename boost::math::tools::promote_args<T>::type ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\
  \
     template <typename T>\
     inline typename boost::math::tools::promote_args<T>::type ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\
  \
     template <class T1, class T2, class T3>\
     inline typename boost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\
  \
     using boost::math::max_factorial;\
     template <class RT>\
     inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\
     using boost::math::unchecked_factorial;\
     template <class RT>\
     inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\
  \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\
  \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\
  \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\
  \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type digamma(T x){ return boost::math::digamma(x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type trigamma(T x){ return boost::math::trigamma(x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\
     \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
     hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\
  \
     template <class RT>\
     inline typename boost::math::tools::promote_args<RT>::type cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type log1p(T x){ return boost::math::log1p(x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type expm1(T x){ return boost::math::expm1(x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::tools::promote_args<T1, T2>::type \
     powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\
  \
     template<typename T>\
     inline typename boost::math::tools::promote_args<T>::type asinh(const T x){ return boost::math::asinh(x, Policy()); }\
  \
     template<typename T>\
     inline typename boost::math::tools::promote_args<T>::type acosh(const T x){ return boost::math::acosh(x, Policy()); }\
  \
     template<typename T>\
     inline typename boost::math::tools::promote_args<T>::type atanh(const T x){ return boost::math::atanh(x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\
     { return boost::math::cyl_bessel_j(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\
     { return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\
     { return boost::math::sph_bessel(v, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\
     { return boost::math::sph_bessel_prime(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\
  \
     template <class T1, class T2>\
     inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
     cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
     sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
     sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\
     { return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\
  \
  template <class OutputIterator, class T>\
     inline void cyl_bessel_j_zero(T v,\
                                   int start_index,\
                                   unsigned number_of_zeros,\
                                   OutputIterator out_it)\
     { boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\
     { return boost::math::cyl_neumann_zero(v, m, Policy()); }\
  \
  template <class OutputIterator, class T>\
     inline void cyl_neumann_zero(T v,\
                                  int start_index,\
                                  unsigned number_of_zeros,\
                                  OutputIterator out_it)\
     { boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type sin_pi(T x){ return boost::math::sin_pi(x); }\
  \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type cos_pi(T x){ return boost::math::cos_pi(x); }\
  \
     using boost::math::fpclassify;\
     using boost::math::isfinite;\
     using boost::math::isinf;\
     using boost::math::isnan;\
     using boost::math::isnormal;\
     using boost::math::signbit;\
     using boost::math::sign;\
     using boost::math::copysign;\
     using boost::math::changesign;\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\
     { return boost::math::expint(z, u, Policy()); }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type expint(T z){ return boost::math::expint(z, Policy()); }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type zeta(T s){ return boost::math::zeta(s, Policy()); }\
     \
     template <class T>\
     inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\
     \
     template <class T>\
     inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\
     \
     template <class T>\
     inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\
     \
     template <class T>\
     inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\
     \
     template <class T>\
     inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\
     \
     template <class T>\
     inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\
     \
     template <class T>\
     inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
     \
     template <class T>\
     inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
     \
     template <class T>\
     inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
     \
     template <int N, class T>\
     inline typename boost::math::tools::promote_args<T>::type pow(T v){ return boost::math::pow<N>(v, Policy()); }\
     \
     template <class T> T nextafter(const T& a, const T& b){ return boost::math::nextafter(a, b, Policy()); }\
     template <class T> T float_next(const T& a){ return boost::math::float_next(a, Policy()); }\
     template <class T> T float_prior(const T& a){ return boost::math::float_prior(a, Policy()); }\
     template <class T> T float_distance(const T& a, const T& b){ return boost::math::float_distance(a, b, Policy()); }\
     template <class T> T ulp(const T& a){ return boost::math::ulp(a, Policy()); }\
     \
     template <class RT1, class RT2>\
     inline typename boost::math::tools::promote_args<RT1, RT2>::type owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\
     \
     template <class T1, class T2>\
     inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\
     {  return boost::math::cyl_hankel_1(v, x, Policy()); }\
     \
     template <class T1, class T2>\
     inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\
     { return boost::math::cyl_hankel_2(v, x, Policy()); }\
     \
     template <class T1, class T2>\
     inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\
     { return boost::math::sph_hankel_1(v, x, Policy()); }\
     \
     template <class T1, class T2>\
     inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\
     { return boost::math::sph_hankel_2(v, x, Policy()); }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\
     { return boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\
     \
     template <class U, class T>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_sn(U k, T theta)\
     { return boost::math::jacobi_sn(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_cn(T k, U theta)\
     { return boost::math::jacobi_cn(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_dn(T k, U theta)\
     { return boost::math::jacobi_dn(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_cd(T k, U theta)\
     { return boost::math::jacobi_cd(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_dc(T k, U theta)\
     { return boost::math::jacobi_dc(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_ns(T k, U theta)\
     { return boost::math::jacobi_ns(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_sd(T k, U theta)\
     { return boost::math::jacobi_sd(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_ds(T k, U theta)\
     { return boost::math::jacobi_ds(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_nc(T k, U theta)\
     { return boost::math::jacobi_nc(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_nd(T k, U theta)\
     { return boost::math::jacobi_nd(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_sc(T k, U theta)\
     { return boost::math::jacobi_sc(k, theta, Policy()); }\
     \
     template <class T, class U>\
     inline typename boost::math::tools::promote_args<T, U>::type jacobi_cs(T k, U theta)\
     { return boost::math::jacobi_cs(k, theta, Policy()); }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type airy_ai(T x)\
     {  return boost::math::airy_ai(x, Policy());  }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type airy_bi(T x)\
     {  return boost::math::airy_bi(x, Policy());  }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type airy_ai_prime(T x)\
     {  return boost::math::airy_ai_prime(x, Policy());  }\
     \
     template <class T>\
     inline typename boost::math::tools::promote_args<T>::type airy_bi_prime(T x)\
     {  return boost::math::airy_bi_prime(x, Policy());  }\
     \
     template <class T>\
     inline T airy_ai_zero(int m)\
     { return boost::math::airy_ai_zero<T>(m, Policy()); }\
     template <class T, class OutputIterator>\
     OutputIterator airy_ai_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
     { return boost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
     \
     template <class T>\
     inline T airy_bi_zero(int m)\
     { return boost::math::airy_bi_zero<T>(m, Policy()); }\
     template <class T, class OutputIterator>\
     OutputIterator airy_bi_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
     { return boost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
     \
     template <class T>\
     T bernoulli_b2n(const int i)\
     { return boost::math::bernoulli_b2n<T>(i, Policy()); }\
     template <class T, class OutputIterator>\
     OutputIterator bernoulli_b2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
     { return boost::math::bernoulli_b2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
     \
     template <class T>\
     T tangent_t2n(const int i)\
     { return boost::math::tangent_t2n<T>(i, Policy()); }\
     template <class T, class OutputIterator>\
     OutputIterator tangent_t2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
     { return boost::math::tangent_t2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
     \
  
  
  
  
  
  #endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP
  
  
  