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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=4, b>=a > For fixed z and a=4, b=6





http://functions.wolfram.com/07.23.03.b3o3.01









  


  








Input Form





Hypergeometric2F1[4, 6, -(29/5), z] == -((1/(2152343750 (-1 + z)^15)) (2152343750 - 41191406250 z + 392060546875 z^2 - 2538251953125 z^3 + 13219541015625 z^4 - 66121740234375 z^5 + 468327275390625 z^6 + 2698864296657273 z^7 + 2194290843124815 z^8 + 383442960294775 z^9 + 4774914894750 z^10 - 82043211250 z^11)) - (1/(9765625 (1 - z)^(79/5))) (379513134 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (7007 + 13475 z + 6125 z^2 + 625 z^3) 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/(9765625 (1 - z)^(79/5))) (379513134 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (7007 + 13475 z + 6125 z^2 + 625 z^3) 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))]) + (759026268 z^(34/5) (7007 + 13475 z + 6125 z^2 + 625 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(9765625 (1 - z)^(79/5)) + (1/(9765625 (1 - z)^(79/5))) (189756567 (-1 + Sqrt[5]) z^(34/5) (7007 + 13475 z + 6125 z^2 + 625 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(9765625 (1 - z)^(79/5))) (189756567 (1 + Sqrt[5]) z^(34/5) (7007 + 13475 z + 6125 z^2 + 625 z^3) 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