Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ap3v)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=4, a₃>=4

For fixed z and a₁=1/2, a₂=4, a₃=4

For fixed z and a₁=1/2, a₂=4, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.ap3v.01

Input Form

HypergeometricPFQ[{1/2, 4, 4}, {-(7/2), -(5/2)}, z] == (1/(8960 (-1 + z)^14)) (8960 - 117248 z + 741632 z^2 - 1451008 z^3 - 294208768 z^4 - 15460189248 z^5 - 112097245008 z^6 - 226017441048 z^7 - 144903929963 z^8 - 27288286168 z^9 - 994787508 z^10) - (1287 (45760 z^(9/2) + 839280 z^(11/2) + 3553960 z^(13/2) + 4795185 z^(15/2) + 2170194 z^(17/2) + 289432 z^(19/2) + 6864 z^(21/2)) ArcSin[Sqrt[z]])/(256 Sqrt[1 - z] (1 - 14 z + 91 z^2 - 364 z^3 + 1001 z^4 - 2002 z^5 + 3003 z^6 - 3432 z^7 + 3003 z^8 - 2002 z^9 + 1001 z^10 - 364 z^11 + 91 z^12 - 14 z^13 + z^14))

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]