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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=-17/8





http://functions.wolfram.com/07.23.03.bl5x.01









  


  








Input Form





Hypergeometric2F1[-(21/8), -(17/8), 1, z] == (2 2^(1/4) (44 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (4729 + 20222 z + 6969 z^2) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (34423 + 104038 Sqrt[1 - z] + 104038 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + (40391 + 444884 Sqrt[1 - z] + 444884 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 3 (-22337 + 51106 Sqrt[1 - z] + 51106 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 7803 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (69615 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4))








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