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

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=3, a₃>=3

For fixed z and a₁=1, a₂=3, a₃=7/2

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

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

Input Form

HypergeometricPFQ[{1, 3, 7/2}, {-(1/2), -(1/2)}, -z] == (40 - 1360 z + 95200 z^2 - 358400 z^3 + 208208 z^4 - 12416 z^5 + 69 z^6 + 18 z^7)/(40 (1 + z)^8) + (21 (128 z^(3/2) - 1792 z^(5/2) + 3360 z^(7/2) - 1120 z^(9/2) + 35 z^(11/2)) ArcSinh[Sqrt[z]])/(8 (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]