Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7x9)

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=-11/2, b>=a

For fixed z and a=-11/2, b=-13/4

http://functions.wolfram.com/07.23.03.a7x9.01

Input Form

Hypergeometric2F1[-(11/2), -(13/4), 4, z] == (2 (22528 - 595584 z + 11707520 z^2 + 812376000 z^3 + 2828383200 z^4 + 2269245816 z^5 + 402290992 z^6 + 1027650 z^7 - 27625 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (22528 - 595584 z + 11707520 z^2 + 812376000 z^3 + 2828383200 z^4 + 2269245816 z^5 + 402290992 z^6 + 1027650 z^7 - 27625 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-22528 + 595584 z - 11707520 z^2 - 812376000 z^3 - 2828383200 z^4 - 2269245816 z^5 - 402290992 z^6 - 1027650 z^7 + 27625 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-22528 + 595584 z - 11707520 z^2 - 812376000 z^3 - 2828383200 z^4 - 2269245816 z^5 - 402290992 z^6 - 1027650 z^7 + 27625 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-22528 + 595584 z - 11707520 z^2 - 812376000 z^3 - 2828383200 z^4 - 2269245816 z^5 - 402290992 z^6 - 1027650 z^7 + 27625 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (22528 - 584320 z + 11418880 z^2 + 384062400 z^3 + 1028772000 z^4 + 616698936 z^5 + 68731000 z^6 - 1005550 z^7 + 27625 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (108483375 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] 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]