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





http://functions.wolfram.com/07.23.03.b0u9.01









  


  










Input Form





Hypergeometric2F1[2, 2, -(27/5), z] == -((-1130976 (-1 + z)^9 z^6 (32 + 5 z) + (1 - z)^10 (883575 - 8606675 z + 38368575 z^2 - 104856675 z^3 + 202590325 z^4 - 326496825 z^5 + 805146693 z^6 + 229893247 z^7) + (1 - z)^9 z (883575 - 8606675 z + 38368575 z^2 - 104856675 z^3 + 202590325 z^4 - 326496825 z^5 + 805146693 z^6 + 229893247 z^7))/(883575 (1 - z)^9 (-1 + z)^9)) + (592 Sqrt[10 - 2 Sqrt[5]] z^(32/5) (37 + 5 z) 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))])/ (125 (1 - z)^(47/5)) - (592 Sqrt[2 (5 + Sqrt[5])] z^(32/5) (37 + 5 z) 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))])/ (125 (1 - z)^(47/5)) + (1184 z^(32/5) (37 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(125 (1 - z)^(47/5)) - (296 (1 + Sqrt[5]) z^(32/5) (37 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(125 (1 - z)^(47/5)) + (296 (-1 + Sqrt[5]) z^(32/5) (37 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(125 (1 - z)^(47/5))










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02