Generalized hypergeometric function 3F2: Differentiation (formula 07.27.20.0008)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Differentiation

Low-order differentiation

With respect to b₁

http://functions.wolfram.com/07.27.20.0008.01

Input Form

Derivative[{0, 0, 0}, {1, 0}, 0][HypergeometricPFQ][ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] == (-((z Product[Subscript[a, j], {j, 1, 3}])/(Subscript[b, 1]^2 Subscript[b, 2]))) HypergeometricPFQ[ {{1 + Subscript[a, 1], 1 + Subscript[a, 2], 1 + Subscript[a, 3]}, {1}, {1, Subscript[b, 1]}}, {{2, 1 + Subscript[b, 1], 1 + Subscript[b, 2]}, {}, {1 + Subscript[b, 1]}}, z, z]

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,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]