Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9696)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=2

http://functions.wolfram.com/07.23.03.9696.01

Input Form

Hypergeometric2F1[-(23/4), 2, 17/4, z] == (1/(1879048192 z^(13/4))) (13 (-2 z^(1/4) (1514205 - 7268184 z + 4710860 z^2 - 29386728 z^3 + 55824174 z^4 - 57086184 z^5 + 33797580 z^6 - 10959960 z^7 + 1514205 z^8) + 1514205 (-1 + z)^8 (1 + 3 z) ArcTan[z^(1/4)] + 1514205 (-1 + z)^8 (1 + 3 z) ArcTanh[z^(1/4)]))

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,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]