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

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, a₂>=1

For fixed z and a₁=1, a₂=5/2, a₃>=5/2

For fixed z and a₁=1, a₂=5/2, a₃=3

For fixed z and a₁=1, a₂=5/2, a₃=3, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1, 5/2, 3}, {-(7/2), 1/2}, -z] == (56 + 744 z + 5072 z^2 + 26784 z^3 + 209232 z^4 - 471208 z^5 + 107368 z^6 - 315 z^7 + 42 z^8)/(56 (1 + z)^9) - (6435 (8 z^(9/2) - 8 z^(11/2) + z^(13/2)) ArcSinh[Sqrt[z]])/ (8 (1 + z)^(19/2))

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]