Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.avf6)

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=4, a₂>=4

For fixed z and a₁=4, a₂=4, a₃>=4

For fixed z and a₁=4, a₂=4, a₃=4

For fixed z and a₁=4, a₂=4, a₃=4, b₁=1

http://functions.wolfram.com/07.27.03.avf6.01

Input Form

HypergeometricPFQ[{4, 4, 4}, {1, 3/2}, -z] == (11913 - 352696 z + 1530176 z^2 - 1552536 z^3 + 368576 z^4 - 12928 z^5)/ (12288 (1 + z)^9) + (5 (25 - 4050 z + 47100 z^2 - 116176 z^3 + 75744 z^4 - 11904 z^5 + 256 z^6) ArcSinh[Sqrt[z]])/(4096 Sqrt[z] (1 + z)^(19/2))

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]