Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0002)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Values at z=1

For fixed a₁, a₂, a₃, b₁, b₂

http://functions.wolfram.com/07.27.03.0002.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, 1] == ((Gamma[Subscript[\[Psi], 3]] Product[Gamma[Subscript[b, k]], {k, 1, 2}])/ Product[Gamma[Subscript[a, k]], {k, 3, 3}]) Sum[(Pochhammer[Subscript[\[Psi], 3], k] HypergeometricPFQExpansionCoefficient[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, k])/(Gamma[Subscript[\[Psi], 3] + Subscript[a, 1] + k] Gamma[Subscript[\[Psi], 3] + Subscript[a, 2] + k]), {k, 0, Infinity}] /; Subscript[\[Psi], 3] == Subscript[b, 1] + Subscript[b, 2] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] && Re[Subscript[\[Psi], 3]] > 0 && Re[Subscript[a, 3]] > 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},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]