hyper_2F1_special_cases()

template<typename Ta1 , typename Ta2 , typename Tb , typename Tz , typename RtnT = boost::optional<return_type_t<Ta1, Ta1, Tb, Tz>>, require_all_arithmetic_t< Ta1, Ta2, Tb, Tz > * = nullptr>

RtnT stan::math::internal::hyper_2F1_special_cases ( const Ta1 &  a1, const Ta2 &  a2, const Tb &  b, const Tz &  z  )

inline

Calculate the Gauss Hypergeometric (2F1) function for special-case combinations of parameters which can be calculated in closed-form.

For more background (and other possible special-cases), see: https://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/03/

The return value is wrapped in a boost::optional<> type so that a void return is possible if no special-case rules are applicable

Template Parameters

Ta1	Type of scalar first 'a' argument
Ta2	Type of scalar second 'a' argument
Tb	Type of scalar 'b' argument
Tz	Type of scalar 'z' argument

Parameters

[in]	a1	First of 'a' arguments to function
[in]	a2	Second of 'a' arguments to function
[in]	b	'b' argument to function
[in]	z	Scalar z argument

Returns

Gauss hypergeometric function

Definition at line 48 of file hypergeometric_2F1.hpp.