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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 5 and fixed z > For fixed z and a=2/5, b>=a > For fixed z and a=2/5, b=1





http://functions.wolfram.com/07.23.03.0314.01









  


  








Input Form





Hypergeometric2F1[2/5, 1, 12/5, z] == 7/(5 z) - ((7 (1 - z))/(50 z^(7/5))) (Log[1 - z] - 5 Log[1 - z^(1/5)] - Sqrt[5] (Log[1 + ((Sqrt[5] + 1)/2) z^(1/5) + z^(2/5)] - Log[1 - ((Sqrt[5] - 1)/2) z^(1/5) + z^(2/5)]) + 2 Sqrt[10 - 2 Sqrt[5]] ArcTan[4 - (Sqrt[5] - 1) z^(1/5), Sqrt[10 + 2 Sqrt[5]] z^(1/5)] - 2 Sqrt[10 + 2 Sqrt[5]] ArcTan[4 + (Sqrt[5] + 1) z^(1/5), Sqrt[10 - 2 Sqrt[5]] z^(1/5)])








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)





2001-10-29