Generalized hypergeometric function 3F2: Differentiation (formula 07.27.20.0031)

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/07.27.20.0031.01

Input Form

D[HypergeometricPFQ[{a + 1, Subscript[a, 2], Subscript[a, 3]}, {a, Subscript[b, 2]}, z], {a, n}] == (((-1)^(n - 1) n!)/a^n) Hypergeometric2F1[Subscript[a, 2], Subscript[a, 3], Subscript[b, 2], z] + (((-1)^n n!)/a^(n + 1)) (a Hypergeometric2F1[Subscript[a, 2], Subscript[a, 3], Subscript[b, 2], z] + ((Subscript[a, 2] Subscript[a, 3])/Subscript[b, 2]) z Hypergeometric2F1[Subscript[a, 2] + 1, Subscript[a, 3] + 1, Subscript[b, 2] + 1, 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)

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]