Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bbu1)

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=-37/8, b>=a

For fixed z and a=-37/8, b=17/8

http://functions.wolfram.com/07.23.03.bbu1.01

Input Form

Hypergeometric2F1[-(37/8), 17/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (457080832 - 2912104832 z + 6983915575 z^2 - 5973798740 z^3 - 4558951670 z^4 + 21185364676 z^5 - 25837119161 z^6 + 16226519320 z^7 - 5364996560 z^8 + 742969920 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (457080832 - 2912104832 z + 6983915575 z^2 - 5973798740 z^3 - 4558951670 z^4 + 21185364676 z^5 - 25837119161 z^6 + 16226519320 z^7 - 5364996560 z^8 + 742969920 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (457080832 - 3197780352 z + 8757112455 z^2 - 10062111150 z^3 - 1414847070 z^4 + 4521610296 z^5 - 5003738481 z^6 + 2954347470 z^7 - 931019760 z^8 + 123828320 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (457080832 - 2912104832 z + 6983915575 z^2 - 5973798740 z^3 - 4558951670 z^4 + 21185364676 z^5 - 25837119161 z^6 + 16226519320 z^7 - 5364996560 z^8 + 742969920 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5207727357267435 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

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]