hypergeometric_1f0() [1/3]

template<typename Ta , typename Tz , typename FvarT = return_type_t<Ta, Tz>, require_all_stan_scalar_t< Ta, Tz > * = nullptr, require_any_fvar_t< Ta, Tz > * = nullptr>

FvarT stan::math::hypergeometric_1f0	(	const Ta &	a,
		const Tz &	z
	)

Returns the Hypergeometric 1F0 function applied to the input arguments: \( _1F_0(a;;z) = \sum_{k=1}^{\infty}\frac{\left(a\right)_kz^k}{k!}\).

\( \frac{\partial _1F_0\left(a;;z\right)}{\partial a} = -\left(1-z\right)^{-a}\log\left(1 - z\right) \)

\( \frac{\partial _1F_0\left(a;;z\right)}{\partial z} = a\left(1-z\right)^{-a-1} \)

Template Parameters

Ta	Fvar or arithmetic type of 'a' argument
Tz	Fvar or arithmetic type of 'z' argument

Parameters

[in]	a	Scalar 'a' argument
[in]	z	Scalar z argument

Returns

Hypergeometric 1F0 function

Definition at line 31 of file hypergeometric_1F0.hpp.