grad_2F1_impl()

template<bool calc_a1, bool calc_a2, bool calc_b1, bool calc_z, typename T1 , typename T2 , typename T3 , typename T_z , typename ScalarT = return_type_t<T1, T2, T3, T_z>, typename TupleT = std::tuple<ScalarT, ScalarT, ScalarT, ScalarT>>

TupleT stan::math::internal::grad_2F1_impl	(	const T1 &	a1,
		const T2 &	a2,
		const T3 &	b1,
		const T_z &	z,
		double	precision = 1e-14,
		int	max_steps = 1e6
	)

Implementation function to calculate the gradients of the hypergeometric function, 2F1.

Calculate the gradients of the hypergeometric function (2F1) as the power series stopping when the series converges to within precision or throwing when the function takes max_steps steps.

This power-series representation converges for all gradients under the same conditions as the 2F1 function itself. As with the hypergeometric_2F1 function, if the parameters do not meet convergence criteria then the gradients are calculated using Euler's transformation.

Template Parameters

calc_a1	boolean for whether to calculate gradients w.r.t a1
calc_a2	boolean for whether to calculate gradients w.r.t a2
calc_b1	boolean for whether to calculate gradients w.r.t b1
calc_z	boolean for whether to calculate gradients w.r.t z
T1	scalar type of a1
T2	scalar type of a2
T3	scalar type of b1
T_z	scalar type of z

Parameters

[in]	a1	see generalized hypergeometric function definition
[in]	a2	see generalized hypergeometric function definition
[in]	b1	see generalized hypergeometric function definition
[in]	z	see generalized hypergeometric function definition
[in]	precision	magnitude of the increment of the infinite sum to truncate the sum
[in]	max_steps	number of steps to take

Returns

Four-element tuple containing gradients w.r.t. to each parameter, as indicated by the calc_* booleans

Definition at line 170 of file grad_2F1.hpp.