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

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=-35/8, b>=a

For fixed z and a=-35/8, b=-31/8

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

Input Form

Hypergeometric2F1[-(35/8), -(31/8), 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (109243008 - 2733635583 z + 50977225530 z^2 + 2185638955495 z^3 + 6312813696140 z^4 + 4232657766687 z^5 + 649984304858 z^6 + 10871471065 z^7) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (109243008 - 2733635583 z + 50977225530 z^2 + 2185638955495 z^3 + 6312813696140 z^4 + 4232657766687 z^5 + 649984304858 z^6 + 10871471065 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (109243008 - 2733635583 z + 50977225530 z^2 + 2185638955495 z^3 + 6312813696140 z^4 + 4232657766687 z^5 + 649984304858 z^6 + 10871471065 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-109243008 + 2774601711 z - 51991137198 z^2 + 1457120353925 z^3 + 9587944855180 z^4 + 11957436361353 z^5 + 3711688476034 z^6 + 215773786403 z^7) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(3710891216267235 Pi (1 + Sqrt[1 - z])^(1/4) 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]