Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ad3m)

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=-11/4, b>=a

For fixed z and a=-11/4, b=-3/4

http://functions.wolfram.com/07.23.03.ad3m.01

Input Form

Hypergeometric2F1[-(11/4), -(3/4), 21/4, z] == (1/(601295421440 z^(17/4))) (663 (-8 (1 - z)^(3/4) z^(1/4) (45045 - 449064 z + 2231152 z^2 - 8594432 z^3 - 37305856 z^4 - 3031040 z^5 + 163840 z^6) - 2310 Sqrt[2] (39 - 420 z + 2240 z^2 - 8960 z^3 + 71680 z^4 + 57344 z^5) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 2310 Sqrt[2] (39 - 420 z + 2240 z^2 - 8960 z^3 + 71680 z^4 + 57344 z^5) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1155 Sqrt[2] (39 - 420 z + 2240 z^2 - 8960 z^3 + 71680 z^4 + 57344 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1155 Sqrt[2] (39 - 420 z + 2240 z^2 - 8960 z^3 + 71680 z^4 + 57344 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]