Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9098)

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=4

For fixed z and a₁=-7/2, a₂=5/2, a₃=4, b₁=-3/2

http://functions.wolfram.com/07.27.03.9098.01

Input Form

HypergeometricPFQ[{-(7/2), 5/2, 4}, {-(3/2), -(1/2)}, -z] == (1/(3 (1 + z)^5)) (3 + 155 z - 11520 z^2 - 231810 z^3 - 1054955 z^4 - 2108502 z^5 - 2148300 z^6 - 1099560 z^7 - 225225 z^8) - 1155 (14 z^(5/2) + 65 z^(7/2)) ArcTan[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]