hypergeometric_2F1() [2/2]

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

return_type_t< Ta1, Ta1, Tb, Tz > stan::math::hypergeometric_2F1 ( const Ta1 &  a1, const Ta2 &  a2, const Tb &  b, const Tz &  z  )

inline

Returns the Gauss hypergeometric function applied to the input arguments: \(_2F_1(a_1,a_2;b;z)\).

If the input parameters do not meet convergence criteria, then Euler's transformation is applied to resolve this: https://mathworld.wolfram.com/EulerTransform.html

For some special-case combinations of parameters the series is calculated in closed form, see the internal::hyper_2F1_special_cases function for more details.

See 'grad_2F1.hpp' for the derivatives wrt each parameter

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 154 of file hypergeometric_2F1.hpp.