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

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=5, b>=a

For fixed z and a=5, b=6

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

Input Form

Hypergeometric2F1[5, 6, -(3/4), z] == (1/134217728) ((1/(-1 + z)^11) (8 (-16777216 + 855638016 z + 26230373535 z^2 + 85126901852 z^3 + 62050999584 z^4 + 9361560192 z^5 + 68913152 z^6)) + (1/(1 - z)^(47/4)) (9085230 Sqrt[2] z^(7/4) (4807 + 34960 z + 55936 z^2 + 23552 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(47/4)) (9085230 Sqrt[2] z^(7/4) (4807 + 34960 z + 55936 z^2 + 23552 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(47/4)) (4542615 Sqrt[2] z^(7/4) (4807 + 34960 z + 55936 z^2 + 23552 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(47/4)) (4542615 Sqrt[2] z^(7/4) (4807 + 34960 z + 55936 z^2 + 23552 z^3 + 2048 z^4) 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]