Generalized hypergeometric function 4F3: Differentiation (formula 07.28.20.0019)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Differentiation

Symbolic differentiation

With respect to a₁

http://functions.wolfram.com/07.28.20.0019.01

Input Form

Derivative[{n, 0, 0, 0}, {0, 0, 0}, 0][HypergeometricPFQ][ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == Sum[((Pochhammer[Subscript[a, 2], k] Pochhammer[Subscript[a, 3], k] Pochhammer[Subscript[a, 4], k])/(Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k] Pochhammer[Subscript[b, 3], k] k!)) D[Pochhammer[Subscript[a, 1], k], {Subscript[a, 1], n}] z^k, {k, 0, Infinity}] /; Abs[z] < 1 && Element[n, Integers] && n > 0

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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]