Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab11)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-15/4

http://functions.wolfram.com/07.23.03.ab11.01

Input Form

Hypergeometric2F1[-(15/4), -(15/4), 13/4, z] == (1/(34359738368 z^(9/4))) (9 (8 (1 - z)^(3/4) z^(1/4) (-148225 + 4150300 z + 267084288 z^2 + 737161216 z^3 + 384164864 z^4 + 31444992 z^5) - 770 Sqrt[2] (385 - 11088 z + 554400 z^2 + 3942400 z^3 + 5068800 z^4 + 1474560 z^5 + 65536 z^6) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 770 Sqrt[2] (385 - 11088 z + 554400 z^2 + 3942400 z^3 + 5068800 z^4 + 1474560 z^5 + 65536 z^6) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 385 Sqrt[2] (385 - 11088 z + 554400 z^2 + 3942400 z^3 + 5068800 z^4 + 1474560 z^5 + 65536 z^6) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 385 Sqrt[2] (385 - 11088 z + 554400 z^2 + 3942400 z^3 + 5068800 z^4 + 1474560 z^5 + 65536 z^6) 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]