Generalized hypergeometric function 3F2: Differentiation (formula 07.27.20.0030)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Differentiation

Symbolic differentiation

With respect to element of parameters ||| With respect to element of parameters

http://functions.wolfram.com/07.27.20.0030.01

Input Form

D[HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3]}, {a + 1, Subscript[b, 2]}, z], {a, n}] == (((-1)^(n - 1) n! z)/(1 + a)^(n + 1)) ((Subscript[a, 2] Subscript[a, 3])/ Subscript[b, 2]) HypergeometricPFQ[{Subscript[c, 1], \[Ellipsis], Subscript[c, n + 1], Subscript[a, 2] + 1, Subscript[a, 3] + 1}, {Subscript[c, 1] + 1, \[Ellipsis], Subscript[c, n + 1] + 1, Subscript[b, 2] + 1}, z] /; Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == a + 1 && 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)

2003-08-21

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,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]