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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=45/8, b>=a > For fixed z and a=45/8, b=47/8





http://functions.wolfram.com/07.23.03.ce0l.01









  


  








Input Form





Hypergeometric2F1[45/8, 47/8, 4, z] == (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-1 + z) (640 - 6865 z + 46995 z^2 + 287309 z^3 + 77425 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 48 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (5 - 55 z - 20865 z^2 - 13037 z^3 + 160 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (80 - 845 z + 209703 z^2 + 182617 z^3 + 13949 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (640 - 6865 z + 46995 z^2 + 287309 z^3 + 77425 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1044291885 Pi (-1 + z)^8 z^3)








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