Generalized hypergeometric function: Differentiation (formula 07.31.20.0018)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.31.20.0018.01

Input Form

D[z^\[Alpha] HypergeometricPFQ[{-(n/r), (-n + 1)/r, \[Ellipsis], (-n + r - 1)/r, Subscript[a, r + 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z^m], {z, n}] == (-1)^n Pochhammer[-\[Alpha], n] z^(\[Alpha] - n) HypergeometricPFQ[{-(n/r), (-n + 1)/r, \[Ellipsis], (-n + r - 1)/r, (\[Alpha] + 1)/m, (\[Alpha] + 2)/m, \[Ellipsis], (\[Alpha] + m)/m, Subscript[a, r + 1], \[Ellipsis], Subscript[a, p]}, {(\[Alpha] - n + 1)/m, (\[Alpha] - n + 2)/m, \[Ellipsis], (\[Alpha] - n + m)/m, Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z^m] /; Element[r, Integers] && r > 0 && Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0

Standard Form

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MathML 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},{b₁,b₂,b₃},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]