Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0336)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For some numeric parameters and fixed z

For fixed z and a₁=1/8, a₂=m/8, a₃=1

http://functions.wolfram.com/07.27.03.0336.01

Input Form

HypergeometricPFQ[{1/8, 3/8, 1}, {9/8, 11/8}, -z] == (3/(32 x^3)) (2 (a x^2 - b) ArcTan[1 - x^2, a x] + 2 (b x^2 + a) ArcTan[1 - x^2, b x] + (b x^2 - a) Log[(1 + b x + x^2)/(1 - b x + x^2)] + (a x^2 + b) Log[(1 + a x + x^2)/(1 - a x + x^2)]) /; a == Sqrt[2 - Sqrt[2]] && b == Sqrt[2 + Sqrt[2]] && x == z^(1/8)

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)

2001-10-29

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]