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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional 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=-43/8, b>=a > For fixed z and a=-43/8, b=-17/8





http://functions.wolfram.com/07.23.03.b7jc.01









  


  










Input Form





Hypergeometric2F1[-(43/8), -(17/8), 2, z] == (1/(721880775 Pi z)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (566181 + 145365767 z + 693342518 z^2 + 470806014 z^3 + 2166225 z^4 - 231285 z^5 + 15300 z^6) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (30007593 + 167182784 z + 128928518 z^2 + 2100180 z^3 - 226695 z^4 + 15300 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4529448 - 27844567 z - 28928986 z^2 - 4516050 z^3 + 240720 z^4 - 24735 z^5 + 1530 z^6) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (566181 + 145365767 z + 693342518 z^2 + 470806014 z^3 + 2166225 z^4 - 231285 z^5 + 15300 z^6) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










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