text: 
  ///////////////////////////////////////////////////////////////////////////////
  // Copyright Christopher Kormanyos 2013 - 2014.
  // Copyright John Maddock 2013.
  // Distributed under 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)
  //
  // This work is based on an earlier work:
  // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
  // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
  //
  
  #include <algorithm>
  #include <cstdint>
  #include <deque>
  #include <functional>
  #include <iostream>
  #include <limits>
  #include <numeric>
  #include <vector>
  #include <boost/math/constants/constants.hpp>
  #include <boost/noncopyable.hpp>
  
  //#define USE_CPP_BIN_FLOAT
  #define USE_CPP_DEC_FLOAT
  //#define USE_MPFR
  
  #if !defined(DIGIT_COUNT)
  #define DIGIT_COUNT 100
  #endif
  
  #if !defined(BOOST_NO_CXX11_HDR_CHRONO)
    #include <chrono>
    #define STD_CHRONO std::chrono
  #else
    #include <boost/chrono.hpp>
    #define STD_CHRONO boost::chrono
  #endif
  
  #if defined(USE_CPP_BIN_FLOAT)
    #include <boost/multiprecision/cpp_bin_float.hpp>
    typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<DIGIT_COUNT + 10> > mp_type;
  #elif defined(USE_CPP_DEC_FLOAT)
    #include <boost/multiprecision/cpp_dec_float.hpp>
    typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<DIGIT_COUNT + 10> > mp_type;
  #elif defined(USE_MPFR)
    #include <boost/multiprecision/mpfr.hpp>
    typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<DIGIT_COUNT + 10> > mp_type;
  #else
    #error no multiprecision floating type is defined
  #endif
  
  template <class clock_type>
  struct stopwatch
  {
  public:
    typedef typename clock_type::duration duration_type;
  
    stopwatch() : m_start(clock_type::now()) { }
  
    stopwatch(const stopwatch& other) : m_start(other.m_start) { }
  
    stopwatch& operator=(const stopwatch& other)
    {
      m_start = other.m_start;
      return *this;
    }
  
    ~stopwatch() { }
  
    duration_type elapsed() const
    {
      return (clock_type::now() - m_start);
    }
  
    void reset()
    {
      m_start = clock_type::now();
    }
  
  private:
    typename clock_type::time_point m_start;
  };
  
  namespace my_math
  {
    template<class T> T chebyshev_t(const std::int32_t n, const T& x);
  
    template<class T> T chebyshev_t(const std::uint32_t n, const T& x, std::vector<T>* vp);
  
    template<class T> bool isneg(const T& x) { return (x < T(0)); }
  
    template<class T> const T& zero() { static const T value_zero(0); return value_zero; }
    template<class T> const T& one () { static const T value_one (1); return value_one; }
    template<class T> const T& two () { static const T value_two (2); return value_two; }
  }
  
  namespace orthogonal_polynomial_series
  {
    template<typename T> static inline T orthogonal_polynomial_template(const T& x, const std::uint32_t n, std::vector<T>* const vp = static_cast<std::vector<T>*>(0u))
    {
      // Compute the value of an orthogonal chebyshev polinomial.
      // Use stable upward recursion.
  
      if(vp != nullptr)
      {
        vp->clear();
        vp->reserve(static_cast<std::size_t>(n + 1u));
      }
  
      T y0 = my_math::one<T>();
  
      if(vp != nullptr) { vp->push_back(y0); }
  
      if(n == static_cast<std::uint32_t>(0u))
      {
        return y0;
      }
  
      T y1 = x;
  
      if(vp != nullptr) { vp->push_back(y1); }
  
      if(n == static_cast<std::uint32_t>(1u))
      {
        return y1;
      }
  
      T a = my_math::two <T>();
      T b = my_math::zero<T>();
      T c = my_math::one <T>();
  
      T yk;
  
      // Calculate higher orders using the recurrence relation.
      // The direction of stability is upward recursion.
      for(std::int32_t k = static_cast<std::int32_t>(2); k <= static_cast<std::int32_t>(n); ++k)
      {
        yk = (((a * x) + b) * y1) - (c * y0);
  
        y0 = y1;
        y1 = yk;
  
        if(vp != nullptr) { vp->push_back(yk); }
      }
  
      return yk;
    }
  }
  
  template<class T> T my_math::chebyshev_t(const std::int32_t n, const T& x)
  {
    if(my_math::isneg(x))
    {
      const bool b_negate = ((n % static_cast<std::int32_t>(2)) != static_cast<std::int32_t>(0));
  
      const T y = chebyshev_t(n, -x);
  
      return (!b_negate ? y : -y);
    }
  
    if(n < static_cast<std::int32_t>(0))
    {
      const std::int32_t nn = static_cast<std::int32_t>(-n);
  
      return chebyshev_t(nn, x);
    }
    else
    {
      return orthogonal_polynomial_series::orthogonal_polynomial_template(x, static_cast<std::uint32_t>(n));
    }
  }
  
  template<class T> T my_math::chebyshev_t(const std::uint32_t n, const T& x, std::vector<T>* const vp) { return orthogonal_polynomial_series::orthogonal_polynomial_template(x, static_cast<std::int32_t>(n),  vp); }
  
  namespace util
  {
    template <class T> float digit_scale()
    {
      const int d = ((std::max)(std::numeric_limits<T>::digits10, 15));
      return static_cast<float>(d) / 300.0F;
    }
  }
  
  namespace examples
  {
    namespace nr_006
    {
      template<typename T> class hypergeometric_pfq_base : private boost::noncopyable
      {
      public:
        virtual ~hypergeometric_pfq_base() { }
  
        virtual void ccoef() const = 0;
  
        virtual T series() const
        {
          using my_math::chebyshev_t;
  
          // Compute the Chebyshev coefficients.
          // Get the values of the shifted Chebyshev polynomials.
          std::vector<T> chebyshev_t_shifted_values;
          const T z_shifted = ((Z / W) * static_cast<std::int32_t>(2)) - static_cast<std::int32_t>(1);
  
          chebyshev_t(static_cast<std::uint32_t>(C.size()),
                      z_shifted,
                      &chebyshev_t_shifted_values);
  
          // Luke: C     ---------- COMPUTE SCALE FACTOR                       ----------
          // Luke: C
          // Luke: C     ---------- SCALE THE COEFFICIENTS                     ----------
          // Luke: C
  
          // The coefficient scaling is preformed after the Chebyshev summation,
          // and it is carried out with a single division operation.
          bool b_neg = false;
  
          const T scale = std::accumulate(C.begin(),
                                          C.end(),
                                          T(0),
                                          [&b_neg](T& scale_sum, const T& ck) -> T
                                          {
                                            ((!b_neg) ? (scale_sum += ck) : (scale_sum -= ck));
                                            b_neg = (!b_neg);
                                            return scale_sum;
                                          });
  
          // Compute the result of the series expansion using unscaled coefficients.
          const T sum = std::inner_product(C.begin(),
                                           C.end(),
                                           chebyshev_t_shifted_values.begin(),
                                           T(0));
  
          // Return the properly scaled result.
          return sum / scale;
        }
  
      protected:
        const   T             Z;
        const   T             W;
        mutable std::deque<T> C;
  
        hypergeometric_pfq_base(const T& z,
                                const T& w) : Z(z),
                                              W(w),
                                              C(0u) { }
  
        virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 500.0F); }
      };
  
      template<typename T> class ccoef4_hypergeometric_0f1 : public hypergeometric_pfq_base<T>
      {
      public:
        ccoef4_hypergeometric_0f1(const T& c,
                                  const T& z,
                                  const T& w) : hypergeometric_pfq_base<T>(z, w),
                                                CP(c) { }
  
        virtual ~ccoef4_hypergeometric_0f1() { }
  
        virtual void ccoef() const
        {
          // See Luke 1977 page 80.
          const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1));
          const std::int32_t N2 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(2));
  
          // Luke: C     ---------- START COMPUTING COEFFICIENTS USING         ----------
          // Luke: C     ---------- BACKWARD RECURRENCE SCHEME                 ----------
          // Luke: C
          T A3(0);
          T A2(0);
          T A1(boost::math::tools::root_epsilon<T>());
  
          hypergeometric_pfq_base<T>::C.resize(1u, A1);
  
          std::int32_t X1 = N2;
  
          T C1 = T(1) - CP;
  
          const T Z1 = T(4) / hypergeometric_pfq_base<T>::W;
  
          for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k)
          {
            const T DIVFAC = T(1) / X1;
  
            --X1;
  
            // The terms have been slightly re-arranged resulting in lower complexity.
            // Parentheses have been added to avoid reliance on operator precedence.
            const T term =   (A2 - ((A3 * DIVFAC) * X1))
                           + ((A2 * X1) * ((1 + (C1 + X1)) * Z1))
                           + ((A1 * X1) * ((DIVFAC - (C1 * Z1)) + (X1 * Z1)));
  
            hypergeometric_pfq_base<T>::C.push_front(term);
  
            A3 = A2;
            A2 = A1;
            A1 = hypergeometric_pfq_base<T>::C.front();
          }
  
          hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2);
        }
  
      private:
        const T CP;
      };
  
      template<typename T> class ccoef1_hypergeometric_1f0 : public hypergeometric_pfq_base<T>
      {
      public:
        ccoef1_hypergeometric_1f0(const T& a,
                                  const T& z,
                                  const T& w) : hypergeometric_pfq_base<T>(z, w),
                                                AP(a) { }
  
        virtual ~ccoef1_hypergeometric_1f0() { }
  
        virtual void ccoef() const
        {
          // See Luke 1977 page 67.
          const std::int32_t N1 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(1));
          const std::int32_t N2 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(2));
  
          // Luke: C     ---------- START COMPUTING COEFFICIENTS USING         ----------
          // Luke: C     ---------- BACKWARD RECURRENCE SCHEME                 ----------
          // Luke: C
          T A2(0);
          T A1(boost::math::tools::root_epsilon<T>());
  
          hypergeometric_pfq_base<T>::C.resize(1u, A1);
  
          std::int32_t X1 = N2;
  
          T V1 = T(1) - AP;
  
          // Here, we have corrected what appears to be an error in Luke's code.
  
          // Luke's original code listing has:
          //  AFAC = 2 + FOUR/W
          // But it appears as though the correct form is:
          //  AFAC = 2 - FOUR/W.
  
          const T AFAC = 2 - (T(4) / hypergeometric_pfq_base<T>::W);
  
          for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k)
          {
            --X1;
  
            // The terms have been slightly re-arranged resulting in lower complexity.
            // Parentheses have been added to avoid reliance on operator precedence.
            const T term = -(((X1 * AFAC) * A1) + ((X1 + V1) * A2)) / (X1 - V1);
  
            hypergeometric_pfq_base<T>::C.push_front(term);
  
            A2 = A1;
            A1 = hypergeometric_pfq_base<T>::C.front();
          }
  
          hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2);
        }
  
      private:
        const T AP;
  
        virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 1600.0F); }
      };
  
      template<typename T> class ccoef3_hypergeometric_1f1 : public hypergeometric_pfq_base<T>
      {
      public:
        ccoef3_hypergeometric_1f1(const T& a,
                                  const T& c,
                                  const T& z,
                                  const T& w) : hypergeometric_pfq_base<T>(z, w),
                                                AP(a),
                                                CP(c) { }
  
        virtual ~ccoef3_hypergeometric_1f1() { }
  
        virtual void ccoef() const
        {
          // See Luke 1977 page 74.
          const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1));
          const std::int32_t N2 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(2));
  
          // Luke: C     ---------- START COMPUTING COEFFICIENTS USING         ----------
          // Luke: C     ---------- BACKWARD RECURRENCE SCHEME                 ----------
          // Luke: C
          T A3(0);
          T A2(0);
          T A1(boost::math::tools::root_epsilon<T>());
  
          hypergeometric_pfq_base<T>::C.resize(1u, A1);
  
          std::int32_t X  = N1;
          std::int32_t X1 = N2;
  
          T XA  =  X + AP;
          T X3A = (X + 3) - AP;
  
          const T Z1 = T(4) / hypergeometric_pfq_base<T>::W;
  
          for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k)
          {
            --X;
            --X1;
            --XA;
            --X3A;
  
            const T X3A_over_X2 = X3A / static_cast<std::int32_t>(X + 2);
  
            // The terms have been slightly re-arranged resulting in lower complexity.
            // Parentheses have been added to avoid reliance on operator precedence.
            const T PART1 =  A1 * (((X + CP) * Z1) - X3A_over_X2);
            const T PART2 =  A2 * (Z1 * ((X + 3) - CP) + (XA / X1));
            const T PART3 =  A3 * X3A_over_X2;
  
            const T term = (((PART1 + PART2) + PART3) * X1) / XA;
  
            hypergeometric_pfq_base<T>::C.push_front(term);
  
            A3 = A2;
            A2 = A1;
            A1 = hypergeometric_pfq_base<T>::C.front();
          }
  
          hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2);
        }
  
      private:
        const T AP;
        const T CP;
      };
  
      template<typename T> class ccoef6_hypergeometric_1f2 : public hypergeometric_pfq_base<T>
      {
      public:
        ccoef6_hypergeometric_1f2(const T& a,
                                  const T& b,
                                  const T& c,
                                  const T& z,
                                  const T& w) : hypergeometric_pfq_base<T>(z, w),
                                                AP(a),
                                                BP(b),
                                                CP(c) { }
  
        virtual ~ccoef6_hypergeometric_1f2() { }
  
        virtual void ccoef() const
        {
          // See Luke 1977 page 85.
          const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1));
  
          // Luke: C     ---------- START COMPUTING COEFFICIENTS USING         ----------
          // Luke: C     ---------- BACKWARD RECURRENCE SCHEME                 ----------
          // Luke: C
          T A4(0);
          T A3(0);
          T A2(0);
          T A1(boost::math::tools::root_epsilon<T>());
  
          hypergeometric_pfq_base<T>::C.resize(1u, A1);
  
          std::int32_t X  = N1;
          T            PP = X + AP;
  
          const T Z1 = T(4) / hypergeometric_pfq_base<T>::W;
  
          for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k)
          {
            --X;
            --PP;
  
            const std::int32_t TWO_X    = static_cast<std::int32_t>(X * 2);
            const std::int32_t X_PLUS_1 = static_cast<std::int32_t>(X + 1);
            const std::int32_t X_PLUS_3 = static_cast<std::int32_t>(X + 3);
            const std::int32_t X_PLUS_4 = static_cast<std::int32_t>(X + 4);
  
            const T QQ = T(TWO_X + 3) / static_cast<std::int32_t>(TWO_X + static_cast<std::int32_t>(5));
            const T SS = (X + BP) * (X + CP);
  
            // The terms have been slightly re-arranged resulting in lower complexity.
            // Parentheses have been added to avoid reliance on operator precedence.
            const T PART1 =   A1 * (((PP - (QQ * (PP + 1))) * 2) + (SS * Z1));
            const T PART2 =  (A2 * (X + 2)) * ((((TWO_X + 1) * PP) / X_PLUS_1) - ((QQ * 4) * (PP + 1)) + (((TWO_X + 3) * (PP + 2)) / X_PLUS_3) + ((Z1 * 2) * (SS - (QQ * (X_PLUS_1 + BP)) * (X_PLUS_1 + CP))));
            const T PART3 =   A3 * ((((X_PLUS_3 - AP) - (QQ * (X_PLUS_4 - AP))) * 2) + (((QQ * Z1) * (X_PLUS_4 - BP)) * (X_PLUS_4 - CP)));
            const T PART4 = ((A4 * QQ) * (X_PLUS_4 - AP)) / X_PLUS_3;
  
            const T term = (((PART1 - PART2) + (PART3 - PART4)) * X_PLUS_1) / PP;
  
            hypergeometric_pfq_base<T>::C.push_front(term);
  
            A4 = A3;
            A3 = A2;
            A2 = A1;
            A1 = hypergeometric_pfq_base<T>::C.front();
          }
  
          hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2);
        }
  
      private:
        const T AP;
        const T BP;
        const T CP;
      };
  
      template<typename T> class ccoef2_hypergeometric_2f1 : public hypergeometric_pfq_base<T>
      {
      public:
        ccoef2_hypergeometric_2f1(const T& a,
                                  const T& b,
                                  const T& c,
                                  const T& z,
                                  const T& w) : hypergeometric_pfq_base<T>(z, w),
                                                AP(a),
                                                BP(b),
                                                CP(c) { }
  
        virtual ~ccoef2_hypergeometric_2f1() { }
  
        virtual void ccoef() const
        {
          // See Luke 1977 page 59.
          const std::int32_t N1 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(1));
          const std::int32_t N2 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(2));
  
          // Luke: C     ---------- START COMPUTING COEFFICIENTS USING         ----------
          // Luke: C     ---------- BACKWARD RECURRENCE SCHEME                 ----------
          // Luke: C
          T A3(0);
          T A2(0);
          T A1(boost::math::tools::root_epsilon<T>());
  
          hypergeometric_pfq_base<T>::C.resize(1u, A1);
  
          std::int32_t X  = N1;
          std::int32_t X1 = N2;
          std::int32_t X3 = static_cast<std::int32_t>((X * 2) + 3);
  
          T X3A = (X + 3) - AP;
          T X3B = (X + 3) - BP;
  
          const T Z1 = T(4) / hypergeometric_pfq_base<T>::W;
  
          for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k)
          {
            --X;
            --X1;
            --X3A;
            --X3B;
            X3 -= 2;
  
            const std::int32_t X_PLUS_2 = static_cast<std::int32_t>(X + 2);
  
            const T XAB = T(1) / ((X + AP) * (X + BP));
  
            // The terms have been slightly re-arranged resulting in lower complexity.
            // Parentheses have been added to avoid reliance on operator precedence.
            const T PART1 = (A1 * X1) * (2 - (((AP + X1) * (BP + X1)) * ((T(X3) / X_PLUS_2) * XAB)) + ((CP + X) * (XAB * Z1)));
            const T PART2 = (A2 * XAB) * ((X3A * X3B) - (X3 * ((X3A + X3B) - 1)) + (((3 - CP) + X) * (X1 * Z1)));
            const T PART3 = (A3 * X1) * (X3A / X_PLUS_2) * (X3B * XAB);
  
            const T term = (PART1 + PART2) - PART3;
  
            hypergeometric_pfq_base<T>::C.push_front(term);
  
            A3 = A2;
            A2 = A1;
            A1 = hypergeometric_pfq_base<T>::C.front();
          }
  
          hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2);
        }
  
      private:
        const T AP;
        const T BP;
        const T CP;
  
        virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 1600.0F); }
      };
  
      template<class T> T luke_ccoef4_hypergeometric_0f1(const T& a, const T& x);
      template<class T> T luke_ccoef1_hypergeometric_1f0(const T& a, const T& x);
      template<class T> T luke_ccoef3_hypergeometric_1f1(const T& a, const T& b, const T& x);
      template<class T> T luke_ccoef6_hypergeometric_1f2(const T& a, const T& b, const T& c, const T& x);
      template<class T> T luke_ccoef2_hypergeometric_2f1(const T& a, const T& b, const T& c, const T& x);
    }
  }
  
  template<class T>
  T examples::nr_006::luke_ccoef4_hypergeometric_0f1(const T& a, const T& x)
  {
    const ccoef4_hypergeometric_0f1<T> hypergeometric_0f1_object(a, x, T(-20));
  
    hypergeometric_0f1_object.ccoef();
  
    return hypergeometric_0f1_object.series();
  }
  
  template<class T>
  T examples::nr_006::luke_ccoef1_hypergeometric_1f0(const T& a, const T& x)
  {
    const ccoef1_hypergeometric_1f0<T> hypergeometric_1f0_object(a, x, T(-20));
  
    hypergeometric_1f0_object.ccoef();
  
    return hypergeometric_1f0_object.series();
  }
  
  template<class T>
  T examples::nr_006::luke_ccoef3_hypergeometric_1f1(const T& a, const T& b, const T& x)
  {
    const ccoef3_hypergeometric_1f1<T> hypergeometric_1f1_object(a, b, x, T(-20));
  
    hypergeometric_1f1_object.ccoef();
  
    return hypergeometric_1f1_object.series();
  }
  
  template<class T>
  T examples::nr_006::luke_ccoef6_hypergeometric_1f2(const T& a, const T& b, const T& c, const T& x)
  {
    const ccoef6_hypergeometric_1f2<T> hypergeometric_1f2_object(a, b, c, x, T(-20));
  
    hypergeometric_1f2_object.ccoef();
  
    return hypergeometric_1f2_object.series();
  }
  
  template<class T>
  T examples::nr_006::luke_ccoef2_hypergeometric_2f1(const T& a, const T& b, const T& c, const T& x)
  {
    const ccoef2_hypergeometric_2f1<T> hypergeometric_2f1_object(a, b, c, x, T(-20));
  
    hypergeometric_2f1_object.ccoef();
  
    return hypergeometric_2f1_object.series();
  }
  
  int main()
  {
    stopwatch<STD_CHRONO::high_resolution_clock> my_stopwatch;
    float total_time = 0.0F;
  
    std::vector<mp_type> hypergeometric_0f1_results(20U);
    std::vector<mp_type> hypergeometric_1f0_results(20U);
    std::vector<mp_type> hypergeometric_1f1_results(20U);
    std::vector<mp_type> hypergeometric_2f1_results(20U);
    std::vector<mp_type> hypergeometric_1f2_results(20U);
  
    const mp_type a(mp_type(3) / 7);
    const mp_type b(mp_type(2) / 3);
    const mp_type c(mp_type(1) / 4);
  
    std::int_least16_t i;
  
    std::cout << "test hypergeometric_0f1." << std::endl;
    i = 1U;
    my_stopwatch.reset();
  
    // Generate a table of values of Hypergeometric0F1.
    // Compare with the Mathematica command:
    // Table[N[HypergeometricPFQ[{}, {3/7}, -(i*EulerGamma)], 100], {i, 1, 20, 1}]
    std::for_each(hypergeometric_0f1_results.begin(),
                  hypergeometric_0f1_results.end(),
                  [&i, &a](mp_type& new_value)
                  {
                    const mp_type x(-(boost::math::constants::euler<mp_type>() * i));
  
                    new_value = examples::nr_006::luke_ccoef4_hypergeometric_0f1(a, x);
  
                    ++i;
                  });
  
    total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count();
  
    // Print the values of Hypergeometric0F1.
    std::for_each(hypergeometric_0f1_results.begin(),
                  hypergeometric_0f1_results.end(),
                  [](const mp_type& h)
                  {
                    std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl;
                  });
  
    std::cout << "test hypergeometric_1f0." << std::endl;
    i = 1U;
    my_stopwatch.reset();
  
    // Generate a table of values of Hypergeometric1F0.
    // Compare with the Mathematica command:
    // Table[N[HypergeometricPFQ[{3/7}, {}, -(i*EulerGamma)], 100], {i, 1, 20, 1}]
    std::for_each(hypergeometric_1f0_results.begin(),
                  hypergeometric_1f0_results.end(),
                  [&i, &a](mp_type& new_value)
                  {
                    const mp_type x(-(boost::math::constants::euler<mp_type>() * i));
  
                    new_value = examples::nr_006::luke_ccoef1_hypergeometric_1f0(a, x);
  
                    ++i;
                  });
  
    total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count();
  
    // Print the values of Hypergeometric1F0.
    std::for_each(hypergeometric_1f0_results.begin(),
                  hypergeometric_1f0_results.end(),
                  [](const mp_type& h)
                  {
                    std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl;
                  });
  
    std::cout << "test hypergeometric_1f1." << std::endl;
    i = 1U;
    my_stopwatch.reset();
  
    // Generate a table of values of Hypergeometric1F1.
    // Compare with the Mathematica command:
    // Table[N[HypergeometricPFQ[{3/7}, {2/3}, -(i*EulerGamma)], 100], {i, 1, 20, 1}]
    std::for_each(hypergeometric_1f1_results.begin(),
                  hypergeometric_1f1_results.end(),
                  [&i, &a, &b](mp_type& new_value)
                  {
                    const mp_type x(-(boost::math::constants::euler<mp_type>() * i));
  
                    new_value = examples::nr_006::luke_ccoef3_hypergeometric_1f1(a, b, x);
  
                    ++i;
                  });
  
    total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count();
  
    // Print the values of Hypergeometric1F1.
    std::for_each(hypergeometric_1f1_results.begin(),
                  hypergeometric_1f1_results.end(),
                  [](const mp_type& h)
                  {
                    std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl;
                  });
  
    std::cout << "test hypergeometric_1f2." << std::endl;
    i = 1U;
    my_stopwatch.reset();
  
    // Generate a table of values of Hypergeometric1F2.
    // Compare with the Mathematica command:
    // Table[N[HypergeometricPFQ[{3/7}, {2/3, 1/4}, -(i*EulerGamma)], 100], {i, 1, 20, 1}]
    std::for_each(hypergeometric_1f2_results.begin(),
                  hypergeometric_1f2_results.end(),
                  [&i, &a, &b, &c](mp_type& new_value)
                  {
                    const mp_type x(-(boost::math::constants::euler<mp_type>() * i));
  
                    new_value = examples::nr_006::luke_ccoef6_hypergeometric_1f2(a, b, c, x);
  
                    ++i;
                  });
  
    total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count();
  
    // Print the values of Hypergeometric1F2.
    std::for_each(hypergeometric_1f2_results.begin(),
                  hypergeometric_1f2_results.end(),
                  [](const mp_type& h)
                  {
                    std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl;
                  });
  
    std::cout << "test hypergeometric_2f1." << std::endl;
    i = 1U;
    my_stopwatch.reset();
  
    // Generate a table of values of Hypergeometric2F1.
    // Compare with the Mathematica command:
    // Table[N[HypergeometricPFQ[{3/7, 2/3}, {1/4}, -(i * EulerGamma)], 100], {i, 1, 20, 1}]
    std::for_each(hypergeometric_2f1_results.begin(),
                  hypergeometric_2f1_results.end(),
                  [&i, &a, &b, &c](mp_type& new_value)
                  {
                    const mp_type x(-(boost::math::constants::euler<mp_type>() * i));
  
                    new_value = examples::nr_006::luke_ccoef2_hypergeometric_2f1(a, b, c, x);
  
                    ++i;
                  });
  
    total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count();
  
    // Print the values of Hypergeometric2F1.
    std::for_each(hypergeometric_2f1_results.begin(),
                  hypergeometric_2f1_results.end(),
                  [](const mp_type& h)
                  {
                    std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl;
                  });
  
    std::cout << "Total execution time = " << std::setprecision(3) << total_time << "s" << std::endl;
  }
  