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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=21/8, b>=a > For fixed z and a=21/8, b=31/8





http://functions.wolfram.com/07.23.03.c84a.01









  


  








Input Form





Hypergeometric2F1[21/8, 31/8, 6, z] == (1/(19684665 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (32768 - 20352 z + 195 z^2) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-2048 + 936 z + 39 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (32768 - 20352 z + 195 z^2) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (4096 - 3664 z + 195 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/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