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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=3, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=3

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

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

Input Form

HypergeometricPFQ[{3/2, 3, 3}, {-(3/2), 7/2}, z] == -((5 (576 - 2808 z + 5452 z^2 - 5309 z^3 + 3034 z^4))/(64 (-1 + z)^5 z^2)) - (15 (-192 + 1064 z - 2420 z^2 + 2871 z^3 - 1848 z^4 + 840 z^5) ArcSin[Sqrt[z]])/(64 Sqrt[1 - z] (-1 + z)^5 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]