Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3856)

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=-3/2, a₃>=-3/2

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

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

http://functions.wolfram.com/07.27.03.3856.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 1}, {-(1/2), 5/2}, z] == (3 (70 + 1205 z - 5229 z^2 - 1015 z^3 + 105 z^4))/(5120 z) + (21 (2 - 15 z + 60 z^2 - 20 z^3 - 30 z^4 + 3 z^5) Log[1 - Sqrt[z]])/ (2048 z^(3/2)) - (21 (2 - 15 z + 60 z^2 - 20 z^3 - 30 z^4 + 3 z^5) Log[1 + Sqrt[z]])/(2048 z^(3/2)) + (315/256) z^(3/2) PolyLog[2, -Sqrt[z]] - (315/256) z^(3/2) PolyLog[2, 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]