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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=3, a₃>=3

For fixed z and a₁=1/2, a₂=3, a₃=4

For fixed z and a₁=1/2, a₂=3, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1/2, 3, 4}, {-(5/2), 7/2}, z] == (-480 + 2896 z - 7278 z^2 + 9615 z^3 - 6370 z^4 - 1848 z^5)/ (128 (-1 + z)^6 z^2) - (3 (-160 + 1072 z - 3098 z^2 + 5057 z^3 - 5148 z^4 + 3432 z^5) ArcSin[Sqrt[z]])/(128 Sqrt[1 - z] (-1 + z)^6 z^(5/2))

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]