Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9392)

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=-3/4

http://functions.wolfram.com/07.23.03.9392.01

Input Form

Hypergeometric2F1[-(23/4), -(3/4), 21/4, z] == (1/(615726511554560 z^(17/4))) (221 (8 (1 - z)^(3/4) z^(1/4) (-19684665 + 287093268 z - 2194453184 z^2 + 13769709184 z^3 + 142053338112 z^4 + 35896115200 z^5 - 7451181056 z^6 + 1548484608 z^7 - 228589568 z^8 + 16777216 z^9) - 3028410 Sqrt[2] (13 - 200 z + 1600 z^2 - 10240 z^3 + 143360 z^4 + 229376 z^5) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 3028410 Sqrt[2] (13 - 200 z + 1600 z^2 - 10240 z^3 + 143360 z^4 + 229376 z^5) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1514205 Sqrt[2] (13 - 200 z + 1600 z^2 - 10240 z^3 + 143360 z^4 + 229376 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1514205 Sqrt[2] (13 - 200 z + 1600 z^2 - 10240 z^3 + 143360 z^4 + 229376 z^5) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - 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,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]