Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0354)

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=3/8, a₂=m/8, a₃=1

http://functions.wolfram.com/07.27.03.0354.01

Input Form

HypergeometricPFQ[{3/8, 7/8, 1}, {11/8, 15/8}, z] == (21/(32 x^7)) (((1 + x^4)/Sqrt[2]) (-Log[(1 + Sqrt[2] x + x^2)/(1 - Sqrt[2] x + x^2)] + 2 ArcTan[1 - x^2, Sqrt[2] x]) - (1 - x^4) (Log[(1 + x)/(1 - x)] - 2 ArcTan[x])) /; x == z^(1/8) && !IntervalMemberQ[Interval[{1, Infinity}], 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)

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]