Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6hh)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-7/8

http://functions.wolfram.com/07.23.03.b6hh.01

Input Form

Hypergeometric2F1[-(45/8), -(7/8), 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (37494912 - 606070101 z + 6540811641 z^2 + 76754106610 z^3 + 31335244850 z^4 - 6290651409 z^5 + 1413186677 z^6 - 229046972 z^7 + 18446736 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (37494912 - 606070101 z + 6540811641 z^2 + 76754106610 z^3 + 31335244850 z^4 - 6290651409 z^5 + 1413186677 z^6 - 229046972 z^7 + 18446736 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (37494912 - 629504421 z + 6915760761 z^2 - 154771116410 z^3 - 286543415510 z^4 - 1113786569 z^5 + 246490517 z^6 - 39089512 z^7 + 3074456 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (37494912 - 606070101 z + 6540811641 z^2 + 76754106610 z^3 + 31335244850 z^4 - 6290651409 z^5 + 1413186677 z^6 - 229046972 z^7 + 18446736 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (232957500830145 Pi Sqrt[Sqrt[2] + 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]