Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ar5l)

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, a₂>=1

For fixed z and a₁=1, a₂=4, a₃>=4

For fixed z and a₁=1, a₂=4, a₃=4

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

http://functions.wolfram.com/07.27.03.ar5l.01

Input Form

HypergeometricPFQ[{1, 4, 4}, {-(7/2), 3}, z] == (1/(672 (-1 + z)^9)) (-672 + 7072 z - 35968 z^2 + 128640 z^3 - 574144 z^4 - 316901 z^5 + 32508 z^6 - 6972 z^7 + 672 z^8) - (2145 (15 z^(9/2) + 2 z^(11/2)) ArcSin[Sqrt[z]])/(32 Sqrt[1 - z] (-1 + z)^9)

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]