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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 4 and fixed z > For fixed z and a=1, b>=a > For fixed z and a=1, b=2





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









  


  








Input Form





Hypergeometric2F1[1, 2, 21/4, z] == (1/(1440 z^(17/4))) (17 (-8 z^(1/4) (-585 + 1287 z - 767 z^2 + 45 z^3) + 1170 Sqrt[2] (1 - z)^(9/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 1170 Sqrt[2] (1 - z)^(9/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 585 Sqrt[2] (1 - z)^(9/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] - 585 Sqrt[2] (1 - z)^(9/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[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