Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.avcf)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

For fixed z and a₁=7/2, a₂=4, a₃=4, b₁=-1/2

http://functions.wolfram.com/07.27.03.avcf.01

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(1/2), 1/2}, -z] == (1/(256 (1 + z)^11)) (256 + 60160 z - 3232576 z^2 + 23361200 z^3 - 44782776 z^4 + 26084177 z^5 - 4206860 z^6 + 119252 z^7) - (315 (1344 z^(3/2) - 25200 z^(5/2) + 104376 z^(7/2) - 132301 z^(9/2) + 53886 z^(11/2) - 6104 z^(13/2) + 112 z^(15/2)) ArcSinh[Sqrt[z]])/ (256 Sqrt[1 + z] (1 + 11 z + 55 z^2 + 165 z^3 + 330 z^4 + 462 z^5 + 462 z^6 + 330 z^7 + 165 z^8 + 55 z^9 + 11 z^10 + z^11))

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)

2007-05-02

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]