Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a888)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=2

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

http://functions.wolfram.com/07.27.03.a888.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 2}, {3, 7/2}, -z] == 40/(1323 z^2) + (Sqrt[1 + z] (-595825 - 704260 z + 16831524 z^2 - 14415232 z^3 + 1572704 z^4))/(21676032 z^2) - (5 (189 - 3150 z - 16800 z^2 + 60480 z^3 - 28800 z^4 + 1792 z^5) ArcSinh[Sqrt[z]])/(344064 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]