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

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=3/2, a₃>=3/2

For fixed z and a₁=-5/2, a₂=3/2, a₃=3

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

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

Input Form

HypergeometricPFQ[{-(5/2), 3/2, 3}, {1/2, 1/2}, z] == (-32 + 1247 z - 3990 z^2 + 2835 z^3)/(32 (-1 + z)) - (15/32) (15 Sqrt[z] - 140 z^(3/2) + 189 z^(5/2)) ArcTanh[Sqrt[z]]

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]