Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7f7)

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=-33/8

http://functions.wolfram.com/07.23.03.b7f7.01

Input Form

Hypergeometric2F1[-(43/8), -(33/8), 1, z] == (1/(721880775 Pi)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (1303699321 + 24071315283 z + 71924749050 z^2 + 49928048742 z^3 + 6872583069 z^4 + 3576375 z^5) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (240626925 + 5281221763 z + 17606311602 z^2 + 13377584022 z^3 + 2016672273 z^4 + 3576375 z^5) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - 2 (1303699321 + 24071315283 z + 71924749050 z^2 + 49928048742 z^3 + 6872583069 z^4 + 3576375 z^5) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-144376155 - 3285096767 z - 12209316960 z^2 - 11847713262 z^3 - 3169062699 z^4 - 166659075 z^5 + 1430550 z^6) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))

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]