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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=41/8, b>=a > For fixed z and a=41/8, b=43/8





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









  


  










Input Form





Hypergeometric2F1[41/8, 43/8, 1, z] == (2 2^(1/4) (8 Sqrt[1 - z] (7482043 + 111770196 z + 255428514 z^2 + 122836692 z^3 + 9403515 z^4) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (7482043 + 111770196 z + 255428514 z^2 + 122836692 z^3 + 9403515 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-1 + z) (13140247 + 147727236 z + 255760362 z^2 + 86716740 z^3 + 3576375 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[1 - z] (7482043 + 111770196 z + 255428514 z^2 + 122836692 z^3 + 9403515 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (16787925 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + z)^10)










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