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

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=-15/4, b>=a

For fixed z and a=-15/4, b=11/2

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

Input Form

Hypergeometric2F1[-(15/4), 11/2, 5, z] == (128 Sqrt[2] (-2 (1 - z)^(1/4) (2816 + 11968 z + 50820 z^2 + 329296 z^3 - 6514825 z^4 + 17082195 z^5 - 16246815 z^6 + 5287425 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (2816 + 11968 z + 50820 z^2 + 329296 z^3 - 6514825 z^4 + 17082195 z^5 - 16246815 z^6 + 5287425 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (2816 + 11968 z + 50820 z^2 + 329296 z^3 - 6514825 z^4 + 17082195 z^5 - 16246815 z^6 + 5287425 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (2816 + 11968 z + 50820 z^2 + 329296 z^3 - 6514825 z^4 + 17082195 z^5 - 16246815 z^6 + 5287425 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (2816 + 11968 z + 50820 z^2 + 329296 z^3 - 6514825 z^4 + 17082195 z^5 - 16246815 z^6 + 5287425 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (2816 + 10560 z + 44572 z^2 + 302632 z^3 - 83895 z^4 - 7748260 z^5 + 19485570 z^6 - 17304300 z^7 + 5287425 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (422463195 Pi Sqrt[1 + Sqrt[1 - z]] 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]