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

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=4, a₃>=4

For fixed z and a₁=5/2, a₂=4, a₃=4

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

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

Input Form

HypergeometricPFQ[{5/2, 4, 4}, {-(5/2), 7/2}, -z] == (1/(2304 z^2 (1 + z)^9)) (-3840 - 33920 z - 130464 z^2 - 270672 z^3 - 193018 z^4 + 2105433 z^5 - 7528788 z^6 + 1829524 z^7) - (5 (-256 - 2432 z - 10336 z^2 - 25840 z^3 - 41990 z^4 - 46189 z^5 + 287430 z^6 - 408408 z^7 + 48048 z^8) ArcSinh[Sqrt[z]])/ (768 Sqrt[1 + z] (z^(5/2) + 9 z^(7/2) + 36 z^(9/2) + 84 z^(11/2) + 126 z^(13/2) + 126 z^(15/2) + 84 z^(17/2) + 36 z^(19/2) + 9 z^(21/2) + z^(23/2)))

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]