Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aua4)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=3

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

http://functions.wolfram.com/07.27.03.aua4.01

Input Form

HypergeometricPFQ[{5/2, 3, 3}, {-(5/2), 7/2}, z] == (3840 - 26240 z + 76384 z^2 - 122192 z^3 + 113786 z^4 - 45667 z^5 + 45134 z^6)/(64 (-1 + z)^7 z^2) + (15 (-256 + 1920 z - 6240 z^2 + 11440 z^3 - 12870 z^4 + 9009 z^5 - 1848 z^6 + 1848 z^7) ArcSin[Sqrt[z]])/(64 Sqrt[1 - z] (-1 + z)^7 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]