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





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









  


  








Input Form





Hypergeometric2F1[2, 2, 17/4, z] == (1/(640 z^(13/4))) (117 (-8 z^(1/4) (-45 + 29 z) - 10 Sqrt[2] (1 - z)^(1/4) (-9 + 4 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 10 Sqrt[2] (1 - z)^(1/4) (-9 + 4 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 5 Sqrt[2] (1 - z)^(1/4) (-9 + 4 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 5 Sqrt[2] (1 - z)^(1/4) (-9 + 4 z) 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