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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=2





http://functions.wolfram.com/07.23.03.az4q.01









  


  








Input Form





Hypergeometric2F1[1, 2, -(26/5), z] == (1/(20020 (-1 + z)^23)) (-76076 (1 - z)^(73/5) (-1 + z) z^(27/5) - 6006 (1 - z)^(38/5) (-1 + z)^8 z^(27/5) + 124124 (-1 + z)^15 z^6 - 4004 (1 - z)^(78/5) z^(22/5) (-2 + 37 z) - 2002 (1 - z)^(43/5) (-1 + z)^7 z^(22/5) (-4 + 39 z) + (-1 + z)^15 (20020 - 167860 z + 627660 z^2 - 1387595 z^3 + 2057225 z^4 - 2363745 z^5 + 5434511 z^6 + 124124 z^7)) - (558 Sqrt[2 (5 + Sqrt[5])] z^(31/5) 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))])/(25 (1 - z)^(41/5)) - (558 Sqrt[10 - 2 Sqrt[5]] z^(31/5) 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))])/(25 (1 - z)^(41/5)) - (1116 z^(31/5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(25 (1 - z)^(41/5)) - (279 (-1 + Sqrt[5]) z^(31/5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(25 (1 - z)^(41/5)) + (279 (1 + Sqrt[5]) z^(31/5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(25 (1 - z)^(41/5))








Standard Form





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MathML Form







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





2007-05-02