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

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=-39/8, b>=a

For fixed z and a=-39/8, b=43/8

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

Input Form

Hypergeometric2F1[-(39/8), 43/8, 5, z] == (65536 2^(1/4) (4 Sqrt[1 - z] (-14237184 - 65698672 z - 308388899 z^2 - 2271553830 z^3 + 62558253625 z^4 - 220130207920 z^5 + 313721575440 z^6 - 203578552320 z^7 + 50082489600 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-14237184 - 65698672 z - 308388899 z^2 - 2271553830 z^3 + 62558253625 z^4 - 220130207920 z^5 + 313721575440 z^6 - 203578552320 z^7 + 50082489600 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[1 - z] (-14237184 - 65698672 z - 308388899 z^2 - 2271553830 z^3 + 62558253625 z^4 - 220130207920 z^5 + 313721575440 z^6 - 203578552320 z^7 + 50082489600 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-28474368 - 113600864 z - 531734723 z^2 - 4142779550 z^3 - 87301026715 z^4 + 620585135660 z^5 - 1482469927120 z^6 + 1678218696960 z^7 - 924495686400 z^8 + 200329958400 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (7055847206983575 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]