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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=6





http://functions.wolfram.com/07.23.03.b1ai.01









  


  










Input Form





Hypergeometric2F1[2, 6, 24/5, z] == (133 (-126 + 155 z + 75 z^2 - 1125 z^3 + 625 z^4))/(156250 (-1 + z)^3 z^3) - (1197 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^6 (-14 + 25 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))])/ (390625 (1 - z)^(46/5) z^(19/5)) - (1197 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^6 (-14 + 25 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))])/ (390625 (1 - z)^(46/5) z^(19/5)) - (2394 (-1 + z)^6 (-14 + 25 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (390625 (1 - z)^(46/5) z^(19/5)) - (1197 (-1 + Sqrt[5]) (-1 + z)^6 (-14 + 25 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(781250 (1 - z)^(46/5) z^(19/5)) + (1197 (1 + Sqrt[5]) (-1 + z)^6 (-14 + 25 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(781250 (1 - z)^(46/5) z^(19/5))










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