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

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=2, a₃>=2

For fixed z and a₁=-1/2, a₂=2, a₃=2

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

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

Input Form

HypergeometricPFQ[{-(1/2), 2, 2}, {-(5/2), -(5/2)}, -z] == (100 + 832 z + 3024 z^2 + 7264 z^3 - 40352 z^4 + 146280 z^5 - 33621 z^6)/ (100 (1 + z)^8) + (63 (-24 z^(7/2) + 280 z^(9/2) - 369 z^(11/2) + 42 z^(13/2)) ArcSinh[Sqrt[z]])/(20 (1 + z)^(17/2))

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]