#ifndef STAN_MATH_PRIM_SCAL_FUN_LOG_FALLING_FACTORIAL_HPP
#define STAN_MATH_PRIM_SCAL_FUN_LOG_FALLING_FACTORIAL_HPP

#include <stan/math/prim/scal/err/check_positive.hpp>
#include <stan/math/prim/scal/fun/is_nan.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <limits>

namespace stan {
  namespace math {

    /**
     *
     * Return the natural log of the falling factorial of the
     * specified arguments.
     *

       \f[
       \mbox{log\_falling\_factorial}(x, n) =
       \begin{cases}
         \textrm{error} & \mbox{if } x \leq 0\\
         \ln (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{log\_falling\_factorial}(x, n)}{\partial x} =
       \begin{cases}
         \textrm{error} & \mbox{if } x \leq 0\\
         \Psi(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{log\_falling\_factorial}(x, n)}{\partial n} =
       \begin{cases}
         \textrm{error} & \mbox{if } x \leq 0\\
         -\Psi(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]

     * @tparam T1 type of first argument
     * @tparam T2 type of second argument
     * @param[in] x First argument
     * @param[in] n Second argument
     * @return log of falling factorial of arguments
     * @throw std::domain_error if the first argument is not
     * positive
     */
    template<typename T1, typename T2>
    inline typename boost::math::tools::promote_args<T1, T2>::type
    log_falling_factorial(const T1 x, const T2 n) {
      if (is_nan(x) || is_nan(n))
        return std::numeric_limits<double>::quiet_NaN();
      static const char* fun = "log_falling_factorial";
      check_positive(fun, "first argument", x);
      return lgamma(x + 1) - lgamma(x - n + 1);
    }

  }
}

#endif
