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

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=-19/8, b>=a

For fixed z and a=-19/8, b=9/8

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

Input Form

Hypergeometric2F1[-(19/8), 9/8, 5, z] == (65536 2^(1/4) (4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (107008 - 618640 z + 1455267 z^2 - 1682450 z^3 + 1725115 z^4 - 743820 z^5 + 128800 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (214016 - 1317536 z + 3352569 z^2 - 4341139 z^3 + 926555 z^4 - 383985 z^5 + 64400 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (107008 - 618640 z + 1455267 z^2 - 1682450 z^3 + 1725115 z^4 - 743820 z^5 + 128800 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 Sqrt[1 - z] (107008 - 618640 z + 1455267 z^2 - 1682450 z^3 + 1725115 z^4 - 743820 z^5 + 128800 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (116222804775 Pi (1 + Sqrt[1 - z])^(1/4) z^4)

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]