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falling_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
3 
4 #include <stan/math/fwd/core.hpp>
5 
7 #include <boost/math/special_functions/digamma.hpp>
8 
9 namespace stan {
10 
11  namespace math {
12 
13  template<typename T>
14  inline fvar<T>
15  falling_factorial(const fvar<T>& x, const fvar<T>& n) {
18 
19  T falling_fact(falling_factorial(x.val_, n.val_));
20  return fvar<T>(falling_fact, falling_fact * digamma(x.val_ + 1) * x.d_
21  - falling_fact * digamma(n.val_ + 1) * n.d_);
22  }
23 
24  template<typename T>
25  inline fvar<T>
26  falling_factorial(const fvar<T>& x, const double n) {
29 
30  T falling_fact(falling_factorial(x.val_, n));
31  return fvar<T>(falling_fact,
32  falling_fact * digamma(x.val_ + 1) * x.d_);
33  }
34 
35  template<typename T>
36  inline fvar<T>
37  falling_factorial(const double x, const fvar<T>& n) {
40 
41  T falling_fact(falling_factorial(x, n.val_));
42  return fvar<T>(falling_fact,
43  -falling_fact * digamma(n.val_ + 1) * n.d_);
44  }
45  }
46 }
47 #endif
fvar< T > falling_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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