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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=2, a₃>=2

For fixed z and a₁=3/2, a₂=2, a₃=4

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

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

Input Form

HypergeometricPFQ[{3/2, 2, 4}, {-(7/2), -(1/2)}, -z] == (1/(224 (1 + z)^11)) (224 + 928 z - 27616 z^2 - 587680 z^3 - 13632320 z^4 + 113536016 z^5 - 142171788 z^6 + 36200451 z^7 - 572880 z^8 - 13860 z^9) - (6435 (-880 z^(9/2) + 3140 z^(11/2) - 2385 z^(13/2) + 378 z^(15/2)) ArcSinh[Sqrt[z]])/(32 Sqrt[1 + z] (1 + 11 z + 55 z^2 + 165 z^3 + 330 z^4 + 462 z^5 + 462 z^6 + 330 z^7 + 165 z^8 + 55 z^9 + 11 z^10 + z^11))

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]