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

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=4

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

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

Input Form

HypergeometricPFQ[{5/2, 3, 4}, {-(3/2), 1/2}, -z] == (1/(384 (1 + z)^10)) (384 + 19200 z + 887680 z^2 - 14406800 z^3 + 34870320 z^4 - 20155961 z^5 + 2433130 z^6 - 12600 z^7) - (1155 (1008 z^(5/2) - 6576 z^(7/2) + 9519 z^(9/2) - 3612 z^(11/2) + 280 z^(13/2)) ArcSinh[Sqrt[z]])/(128 (1 + z)^(21/2))

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]