Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9957)

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=4

http://functions.wolfram.com/07.23.03.9957.01

Input Form

Hypergeometric2F1[-(23/4), 4, 21/4, z] == (1/(1443109011456 z^(17/4))) (221 (-2 z^(1/4) (-19684665 + 11205117 z + 23554300 z^2 + 89506340 z^3 - 1613149902 z^4 + 4847308374 z^5 - 6793638708 z^6 + 5119586100 z^7 - 2018435265 z^8 + 328582485 z^9) + 1514205 (-1 + z)^7 (13 + 81 z + 279 z^2 + 651 z^3) ArcTan[z^(1/4)] + 1514205 (-1 + z)^7 (13 + 81 z + 279 z^2 + 651 z^3) 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]