Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7598)

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=-7/2, a₂>=-7/2

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

For fixed z and a₁=-7/2, a₂=3/2, a₃=2

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

http://functions.wolfram.com/07.27.03.7598.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 2}, {7/2, 4}, z] == -((40 (4 + 39 z))/(429 z^3)) + (Sqrt[1 - z] (40960 + 284705 z - 55230 z^2 + 80192 z^3 - 49328 z^4 + 16320 z^5 - 2304 z^6))/(109824 z^3) + (105 (3 + 4 z) ArcSin[Sqrt[z]])/ (256 z^(5/2))

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]