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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=1/2, a₃>=1/2

For fixed z and a₁=1/2, a₂=1/2, a₃=3

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

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

Input Form

HypergeometricPFQ[{1/2, 1/2, 3}, {5/2, 4}, -z] == -(16/(25 z^3)) + (Sqrt[1 + z] (32 - 16 z - 63 z^2))/(50 z^3) + (3 (5 + 6 z) ArcSinh[Sqrt[z]])/(10 z^(3/2))

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]