Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba0c)

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=-3/8

http://functions.wolfram.com/07.23.03.ba0c.01

Input Form

Hypergeometric2F1[-(39/8), -(3/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-911179776 + 11791947648 z - 74470047197 z^2 + 323336320125 z^3 - 1315829186490 z^4 - 6963596127334 z^5 - 234995122593 z^6 + 47800154457 z^7 - 7198587000 z^8 + 543533760 z^9) 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) (-911179776 + 11791947648 z - 74470047197 z^2 + 323336320125 z^3 - 1315829186490 z^4 - 6963596127334 z^5 - 234995122593 z^6 + 47800154457 z^7 - 7198587000 z^8 + 543533760 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-911179776 + 11791947648 z - 74470047197 z^2 + 323336320125 z^3 - 1315829186490 z^4 - 6963596127334 z^5 - 234995122593 z^6 + 47800154457 z^7 - 7198587000 z^8 + 543533760 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-911179776 + 12133640064 z - 78798596045 z^2 + 350103088062 z^3 - 1430054085915 z^4 + 11787021848756 z^5 + 6639106913901 z^6 - 1028649773250 z^7 + 204766719003 z^8 - 29836121040 z^9 + 2174135040 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(4793742592424640855 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]