Regularized generalized hypergeometric function: Differentiation (formula 07.32.20.0007)

HypergeometricPFQRegularized

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]

Differentiation

Symbolic differentiation

With respect to a₁

http://functions.wolfram.com/07.32.20.0007.01

Input Form

Derivative[{n, 0, \[Ellipsis], 0}, {0, \[Ellipsis], 0}, 0][ HypergeometricPFQRegularized][{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == Sum[(Product[Pochhammer[Subscript[a, j], k], {j, 2, p}]/ (k! Product[Gamma[Subscript[b, j] + k], {j, 1, q}])) D[Pochhammer[Subscript[a, 1], k], {Subscript[a, 1], n}] z^k, {k, 0, Infinity}] /; (Element[n, Integers] && n > 0 && q == p - 1 && Abs[z] < 1) || q >= p

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]