Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ave5)

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=-7/2

http://functions.wolfram.com/07.27.03.ave5.01

Input Form

HypergeometricPFQ[{4, 4, 4}, {-(7/2), 3}, -z] == (1/(10752 (1 + z)^12)) (10752 + 194560 z + 1905664 z^2 + 15538176 z^3 + 206353920 z^4 - 1065905367 z^5 + 906385320 z^6 - 172690504 z^7 + 4956344 z^8) - (2145 (10725 z^(9/2) - 25610 z^(11/2) + 13860 z^(13/2) - 1776 z^(15/2) + 32 z^(17/2)) ArcSinh[Sqrt[z]])/ (512 Sqrt[1 + z] (1 + 12 z + 66 z^2 + 220 z^3 + 495 z^4 + 792 z^5 + 924 z^6 + 792 z^7 + 495 z^8 + 220 z^9 + 66 z^10 + 12 z^11 + z^12))

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]