Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7978)

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=3/2, a₃>=3/2

For fixed z and a₁=-7/2, a₂=3/2, a₃=4

For fixed z and a₁=-7/2, a₂=3/2, a₃=4, b₁=-3/2

http://functions.wolfram.com/07.27.03.7978.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 4}, {-(3/2), -(3/2)}, z] == (1/(6 (-1 + z)^5)) (-6 + 86 z - 3840 z^2 + 140865 z^3 - 734470 z^4 + 1562616 z^5 - 1650726 z^6 + 865095 z^7 - 180180 z^8) + (1155/2) (-7 z^(5/2) + 52 z^(7/2)) 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]