Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5b6)

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=19/8

http://functions.wolfram.com/07.23.03.b5b6.01

Input Form

Hypergeometric2F1[-(47/8), 19/8, 4, z] == (2048 2^(1/4) (-2 Sqrt[1 - z] (-55762304 + 124158255 z + 289702595 z^2 - 2865284035 z^3 + 6843951105 z^4 - 8265399728 z^5 + 5587021440 z^6 - 2024006400 z^7 + 307632000 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-55762304 + 124158255 z + 289702595 z^2 - 2865284035 z^3 + 6843951105 z^4 - 8265399728 z^5 + 5587021440 z^6 - 2024006400 z^7 + 307632000 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-55762304 + 124158255 z + 289702595 z^2 - 2865284035 z^3 + 6843951105 z^4 - 8265399728 z^5 + 5587021440 z^6 - 2024006400 z^7 + 307632000 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-55762304 + 159009695 z + 217821500 z^2 + 2700055290 z^3 - 11749254620 z^4 + 21622149967 z^5 - 22216007320 z^6 + 13325080080 z^7 - 4386408000 z^8 + 615264000 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5894609195475 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)

Standard Form

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MathML Form

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</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]