Automatic Differentiation
 
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lgamma_stirling.hpp
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1#ifndef STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_HPP
2#define STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_HPP
3
4#include <stan/math/prim/meta.hpp>
5#include <stan/math/prim/fun/constants.hpp>
6#include <stan/math/prim/fun/lgamma.hpp>
7#include <stan/math/prim/fun/log.hpp>
8#include <cmath>
9
10namespace stan {
11namespace math {
12
25template <typename T>
26return_type_t<T> lgamma_stirling(const T x) {
27 return HALF_LOG_TWO_PI + (x - 0.5) * log(x) - x;
28}
29
30} // namespace math
31} // namespace stan
32
33#endif
stan::return_type_t
typename return_type< Ts... >::type return_type_t
Convenience type for the return type of the specified template parameters.
Definition return_type.hpp:218
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition log.hpp:15
stan::math::lgamma_stirling
return_type_t< T > lgamma_stirling(const T x)
Return the Stirling approximation to the lgamma function.
Definition lgamma_stirling.hpp:26
stan::math::HALF_LOG_TWO_PI
static constexpr double HALF_LOG_TWO_PI
The value of half the natural logarithm , .
Definition constants.hpp:181
stan
The lgamma implementation in stan-math is based on either the reentrant safe lgamma_r implementation ...
Definition unit_vector_constrain.hpp:15