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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.aje3.01









  


  








Input Form





Hypergeometric2F1[1, 2, 1/4, z] == (1/(32 (1 - z)^(11/4))) (32 (1 - z)^(3/4) + 24 (1 - z)^(3/4) z - 42 Sqrt[2] z^(3/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 42 Sqrt[2] z^(3/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 21 Sqrt[2] z^(3/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 21 Sqrt[2] z^(3/4) 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