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

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, a₂>=3

For fixed z and a₁=3, a₂=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=3

For fixed z and a₁=3, a₂=3, a₃=3, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3, 3, 3}, {-(7/2), 4}, -z] == (1/(1120 z^2 (1 + z)^8)) (-540540 - 4144140 z - 13788656 z^2 - 25921072 z^3 - 29933960 z^4 - 21434408 z^5 - 8348464 z^6 - 3139025 z^7) + (3 (360360 + 3003000 z + 11002992 z^2 + 23186592 z^3 + 30807920 z^4 + 26533520 z^5 + 14574720 z^6 + 4322027 z^7 + 974822 z^8) ArcSinh[Sqrt[z]])/(1120 Sqrt[1 + z] (z^(5/2) + 8 z^(7/2) + 28 z^(9/2) + 56 z^(11/2) + 70 z^(13/2) + 56 z^(15/2) + 28 z^(17/2) + 8 z^(19/2) + z^(21/2))) - (3861 ArcSinh[Sqrt[z]]^2)/(8 z^3)

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]