Generalized hypergeometric function 2F2: Differentiation (formula 07.25.20.0025)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.25.20.0025.02

Input Form

D[HypergeometricPFQ[{-n, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z]/E^z, {z, n}] == ((-1)^n Sum[((Pochhammer[-n, k] z^k)/(k! Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k])) HypergeometricPFQ[ {-n, k - n, Subscript[a, 2] + k}, {Subscript[b, 1] + k, Subscript[b, 2] + k}, z], {k, 0, n}])/E^z /; 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,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]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]