Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a93n)

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=2

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

http://functions.wolfram.com/07.27.03.a93n.01

Input Form

HypergeometricPFQ[{-(5/2), -(3/2), 2}, {5/2, 3}, -z] == 8/(735 z^2) + (Sqrt[1 + z] (-4096 - 8977 z + 293934 z^2 - 192760 z^3 + 3920 z^4))/(376320 z^2) + (3 (35 + 280 z - 1008 z^2 + 320 z^3) ArcSinh[Sqrt[z]])/(3584 z^(3/2))

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]