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

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.avcr.01

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {1/2, 1/2}, -z] == (768 - 152592 z + 2095640 z^2 - 6186826 z^3 + 5012889 z^4 - 1062376 z^5 + 38444 z^6)/(768 (1 + z)^10) - (1/(256 (1 + z)^(21/2))) (35 (112 Sqrt[z] - 4872 z^(3/2) + 33558 z^(5/2) - 61483 z^(7/2) + 33558 z^(9/2) - 4872 z^(11/2) + 112 z^(13/2)) ArcSinh[Sqrt[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)

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]