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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=15/8, b>=a > For fixed z and a=15/8, b=21/8





http://functions.wolfram.com/07.23.03.c57m.01









  


  








Input Form





Hypergeometric2F1[15/8, 21/8, 6, z] == (1/(72747675 Pi z^5)) (524288 2^(1/4) (1 + Sqrt[1 - z])^(1/4) (2 Sqrt[2] (-98304 + 177792 z - 82057 z^2 + 4389 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (12288 (8 Sqrt[2] + 5 Sqrt[1 + Sqrt[1 - z]] + 3 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) - 48 (3704 Sqrt[2] + 2105 Sqrt[1 + Sqrt[1 - z]] + 831 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) z + (82057 Sqrt[2] + 37780 Sqrt[1 + Sqrt[1 - z]] + 4389 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) z^2 - 4389 Sqrt[2] z^3) 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