Generalized hypergeometric function 4F3: Differentiation (formula 07.28.20.0012)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Differentiation

Low-order differentiation

With respect to b₂

http://functions.wolfram.com/07.28.20.0012.01

Input Form

Derivative[{0, 0, 0, 0}, {0, 1, 0}, 0][HypergeometricPFQ][ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == (-((z Product[Subscript[a, j], {j, 1, 4}])/(Subscript[b, 2] Product[Subscript[b, j], {j, 1, 3}]))) HypergeometricPFQ[{{1 + Subscript[a, 1], 1 + Subscript[a, 2], 1 + Subscript[a, 3], 1 + Subscript[a, 4]}, {1}, {1, Subscript[b, 2]}}, {{2, 1 + Subscript[b, 1], 1 + Subscript[b, 2], 1 + Subscript[b, 3]}, {}, {1 + Subscript[b, 2]}}, 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},{b₁,b₂},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]