Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3220)

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=-5/2, a₃>=-5/2

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

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3, b₁=1

http://functions.wolfram.com/07.27.03.3220.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 3}, {1, 7/2}, -z] == -((3 Sqrt[1 + z] (105 - 770 z - 656528 z^2 + 3883984 z^3 - 2189888 z^4 + 42240 z^5))/(2097152 z^2)) - (105 (-3 + 20 z - 1200 z^2 + 48000 z^3 - 112000 z^4 + 32256 z^5) ArcSinh[Sqrt[z]])/(2097152 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]