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

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=3

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

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

Input Form

HypergeometricPFQ[{3/2, 2, 3}, {-(5/2), -(3/2)}, -z] == (1/(80 (1 + z)^10)) (80 + 608 z + 5520 z^2 + 397760 z^3 - 10381600 z^4 + 33971760 z^5 - 24442152 z^6 + 3537345 z^7 - 22050 z^8) - (693 (576 z^(7/2) - 5392 z^(9/2) + 10008 z^(11/2) - 4599 z^(13/2) + 420 z^(15/2)) ArcSinh[Sqrt[z]])/(16 (1 + z)^(21/2))

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]