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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=11/8, b>=a > For fixed z and a=11/8, b=15/8





http://functions.wolfram.com/07.23.03.c39l.01









  


  








Input Form





Hypergeometric2F1[11/8, 15/8, 6, z] == -((524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-32768 + 90240 z - 80195 z^2 + 22135 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (32768 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 384 (267 + 235 Sqrt[1 - z] + 235 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 5 (22135 + 16039 Sqrt[1 - z] + 16039 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 5 (8948 + 4427 Sqrt[1 - z] + 4427 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 + 3825 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (70659225 Pi (1 + Sqrt[1 - z])^(1/4) (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