text: #ifndef STAN_MATH_PRIM_SCAL_FUN_FALLING_FACTORIAL_HPP
  #define STAN_MATH_PRIM_SCAL_FUN_FALLING_FACTORIAL_HPP
  
  #include <boost/math/special_functions/factorials.hpp>
  #include <stan/math/prim/scal/fun/boost_policy.hpp>
  #include <stan/math/prim/scal/err/check_not_nan.hpp>
  #include <stan/math/prim/scal/err/check_nonnegative.hpp>
  #include <limits>
  
  namespace stan {
  namespace math {
  
  /**
   * Return the falling factorial function evaluated
   * at the inputs.
   * Will throw for NaN x and for negative n
   *
   * @tparam T Type of x argument.
   * @param x Argument.
   * @param n Argument
   * @return Result of falling factorial function.
   * @throw std::domain_error if x is NaN
   * @throw std::domain_error if n is negative
   *
     \f[
     \mbox{falling\_factorial}(x, n) =
     \begin{cases}
       \textrm{error} & \mbox{if } x \leq 0\\
       (x)_n & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt]
       \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN}
     \end{cases}
     \f]
  
     \f[
     \frac{\partial\, \mbox{falling\_factorial}(x, n)}{\partial x} =
     \begin{cases}
       \textrm{error} & \mbox{if } x \leq 0\\
       \frac{\partial\, (x)_n}{\partial x} & \mbox{if } x > 0 \textrm{ and }
   -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or
   } n = \textrm{NaN} \end{cases} \f]
  
     \f[
     \frac{\partial\, \mbox{falling\_factorial}(x, n)}{\partial n} =
     \begin{cases}
       \textrm{error} & \mbox{if } x \leq 0\\
       \frac{\partial\, (x)_n}{\partial n} & \mbox{if } x > 0 \textrm{ and }
   -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or
   } n = \textrm{NaN} \end{cases} \f]
  
     \f[
     (x)_n=\frac{\Gamma(x+1)}{\Gamma(x-n+1)}
     \f]
  
     \f[
     \frac{\partial \, (x)_n}{\partial x} = (x)_n\Psi(x+1)
     \f]
  
     \f[
     \frac{\partial \, (x)_n}{\partial n} = -(x)_n\Psi(n+1)
     \f]
   *
   */
  template <typename T>
  inline typename boost::math::tools::promote_args<T>::type falling_factorial(
      const T& x, int n) {
    static const char* function = "falling_factorial";
    check_not_nan(function, "first argument", x);
    check_nonnegative(function, "second argument", n);
    return boost::math::falling_factorial(x, n, boost_policy_t());
  }
  
  }  // namespace math
  }  // namespace stan
  
  #endif
  