Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b938)

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=-41/8, b>=a

For fixed z and a=-41/8, b=11/8

http://functions.wolfram.com/07.23.03.b938.01

Input Form

Hypergeometric2F1[-(41/8), 11/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-117765120 + 931080480 z - 3034406925 z^2 + 4395491100 z^3 - 28038917270 z^4 + 36873523596 z^5 - 28525500549 z^6 + 13523051360 z^7 - 3647105280 z^8 + 430510080 z^9) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 4 (-29441280 + 243810600 z - 842871645 z^2 + 1361084175 z^3 - 2064801830 z^4 + 2575290354 z^5 - 1922521965 z^6 + 885533831 z^7 - 232989120 z^8 + 26906880 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-117765120 + 931080480 z - 3034406925 z^2 + 4395491100 z^3 - 28038917270 z^4 + 36873523596 z^5 - 28525500549 z^6 + 13523051360 z^7 - 3647105280 z^8 + 430510080 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-117765120 + 931080480 z - 3034406925 z^2 + 4395491100 z^3 - 28038917270 z^4 + 36873523596 z^5 - 28525500549 z^6 + 13523051360 z^7 - 3647105280 z^8 + 430510080 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (693482125210875 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^4)

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]