Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av10)

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=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

For fixed z and a₁=3, a₂=7/2, a₃=4, b₁=-5/2

http://functions.wolfram.com/07.27.03.av10.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(5/2), 5/2}, z] == (1/(3200 (-1 + z)^10)) (3200 - 53504 z + 543360 z^2 - 7700480 z^3 - 37380100 z^4 - 25318845 z^5 - 2832066 z^6 - 9240 z^7) - (9009 z^(7/2) (396 + 847 z + 348 z^2 + 24 z^3) ArcSin[Sqrt[z]])/ (640 Sqrt[1 - z] (-1 + z)^10)

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]