Automatic Differentiation
 
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◆ hypergeometric_1f0() [2/3]

template<typename Ta , typename Tz , require_all_arithmetic_t< Ta, Tz > * = nullptr>
return_type_t< Ta, Tz > 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
TaArithmetic type of 'a' argument
TzArithmetic type of 'z' argument
Parameters
[in]aScalar 'a' argument
[in]zScalar z argument
Returns
Hypergeometric 1F0 function

Definition at line 31 of file hypergeometric_1F0.hpp.