Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b89r)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-43/8, b>=a

For fixed z and a=-43/8, b=41/8

http://functions.wolfram.com/07.23.03.b89r.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6588288 + 60787251 z + 696196746 z^2 - 74464843429 z^3 + 442989131696 z^4 - 1044395951872 z^5 + 1207880826880 z^6 - 686877900800 z^7 + 154103971840 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (6588288 + 58316643 z + 672725970 z^2 - 27358378345 z^3 + 140885095460 z^4 - 304581242368 z^5 + 330736387072 z^6 - 178943098880 z^7 + 38525992960 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6588288 + 60787251 z + 696196746 z^2 - 74464843429 z^3 + 442989131696 z^4 - 1044395951872 z^5 + 1207880826880 z^6 - 686877900800 z^7 + 154103971840 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (6588288 + 60787251 z + 696196746 z^2 - 74464843429 z^3 + 442989131696 z^4 - 1044395951872 z^5 + 1207880826880 z^6 - 686877900800 z^7 + 154103971840 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (48511109960775 Pi (1 + Sqrt[1 - z])^(1/4) z^3)

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]