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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=5, b>=a > For fixed z and a=5, b=5





http://functions.wolfram.com/07.23.03.b48a.01









  


  








Input Form





Hypergeometric2F1[5, 5, -(1/5), z] == -((1/(781250 (-1 + z)^10)) (-781250 + 105468750 z + 1137450827 z^2 + 2077266575 z^3 + 839617275 z^4 + 54739375 z^5)) + (1/(1953125 (1 - z)^(51/5))) (12012 Sqrt[2 (5 + Sqrt[5])] z^(6/5) (4004 + 29120 z + 40950 z^2 + 13000 z^3 + 625 z^4) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) + (1/(1953125 (1 - z)^(51/5))) (12012 Sqrt[10 - 2 Sqrt[5]] z^(6/5) (4004 + 29120 z + 40950 z^2 + 13000 z^3 + 625 z^4) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) + (24024 z^(6/5) (4004 + 29120 z + 40950 z^2 + 13000 z^3 + 625 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(51/5)) + (1/(1953125 (1 - z)^(51/5))) (6006 (-1 + Sqrt[5]) z^(6/5) (4004 + 29120 z + 40950 z^2 + 13000 z^3 + 625 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(1953125 (1 - z)^(51/5))) (6006 (1 + Sqrt[5]) z^(6/5) (4004 + 29120 z + 40950 z^2 + 13000 z^3 + 625 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])








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)





2007-05-02