Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8a1)

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.b8a1.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (562200576 + 366748032 z + 499114287 z^2 + 1184261925 z^3 + 5958368745 z^4 - 348191361741 z^5 + 1358921979568 z^6 - 2267746254592 z^7 + 1955410329600 z^8 - 861258711040 z^9 + 154103971840 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (562200576 + 155922816 z + 303936255 z^2 + 928862823 z^3 + 5423070345 z^4 - 120208287891 z^5 + 413009011684 z^6 - 641576565760 z^7 + 525792863232 z^8 - 222538301440 z^9 + 38525992960 z^10) 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) (562200576 + 366748032 z + 499114287 z^2 + 1184261925 z^3 + 5958368745 z^4 - 348191361741 z^5 + 1358921979568 z^6 - 2267746254592 z^7 + 1955410329600 z^8 - 861258711040 z^9 + 154103971840 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (562200576 + 366748032 z + 499114287 z^2 + 1184261925 z^3 + 5958368745 z^4 - 348191361741 z^5 + 1358921979568 z^6 - 2267746254592 z^7 + 1955410329600 z^8 - 861258711040 z^9 + 154103971840 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(60396331901164875 Pi (1 + Sqrt[1 - z])^(1/4) 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]