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





http://functions.wolfram.com/07.23.03.azg6.01









  


  








Input Form





Hypergeometric2F1[1, 5, -(21/5), z] == (1/(1155000 (-1 + z)^10)) (1155000 - 12925000 z + 68303125 z^2 - 234459375 z^3 + 660284375 z^4 - 4266138125 z^5 - 523134612 z^6 + 109769660 z^7 - 18118100 z^8 + 1501500 z^9) + (1140087 Sqrt[2 (5 + Sqrt[5])] z^(26/5) 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))])/ (3125 (1 - z)^(51/5)) + (1140087 Sqrt[10 - 2 Sqrt[5]] z^(26/5) 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))])/ (3125 (1 - z)^(51/5)) + (2280174 z^(26/5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (3125 (1 - z)^(51/5)) + (1140087 (-1 + Sqrt[5]) z^(26/5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(6250 (1 - z)^(51/5)) - (1140087 (1 + Sqrt[5]) z^(26/5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(6250 (1 - z)^(51/5))








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