Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5kw)

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=-47/8, b>=a

For fixed z and a=-47/8, b=35/8

http://functions.wolfram.com/07.23.03.b5kw.01

Input Form

Hypergeometric2F1[-(47/8), 35/8, 3, z] == (256 2^(1/4) (-4 Sqrt[1 - z] (1742572 + 33544511 z - 1973617494 z^2 + 12016274795 z^3 - 29134389200 z^4 + 34487085360 z^5 - 19983774720 z^6 + 4552953600 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (1742572 + 33544511 z - 1973617494 z^2 + 12016274795 z^3 - 29134389200 z^4 + 34487085360 z^5 - 19983774720 z^6 + 4552953600 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[1 - z] (1742572 + 33544511 z - 1973617494 z^2 + 12016274795 z^3 - 29134389200 z^4 + 34487085360 z^5 - 19983774720 z^6 + 4552953600 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (3485144 + 64910807 z + 2060281982 z^2 - 25624024385 z^3 + 99218798980 z^4 - 183663924080 z^5 + 179681698560 z^6 - 89951596800 z^7 + 18211814400 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (774375036435 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^2)

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]