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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=5, b>=a > For fixed z and a=5, b=6





http://functions.wolfram.com/07.23.03.b4ca.01









  


  








Input Form





Hypergeometric2F1[5, 6, 24/5, z] == (399 (63 - 415 z + 1275 z^2 + 45875 z^3 + 1250 z^4))/ (19531250 (-1 + z)^6 z^3) - (1197 Sqrt[2 (5 + Sqrt[5])] (-21 + 150 z - 500 z^2 + 1250 z^3 + 3125 z^4) 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))])/ (48828125 (1 - z)^(31/5) z^(19/5)) - (1197 Sqrt[10 - 2 Sqrt[5]] (-21 + 150 z - 500 z^2 + 1250 z^3 + 3125 z^4) 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))])/ (48828125 (1 - z)^(31/5) z^(19/5)) - (2394 (-21 + 150 z - 500 z^2 + 1250 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(48828125 (1 - z)^(31/5) z^(19/5)) - (1197 (-1 + Sqrt[5]) (-21 + 150 z - 500 z^2 + 1250 z^3 + 3125 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(97656250 (1 - z)^(31/5) z^(19/5)) + (1197 (1 + Sqrt[5]) (-21 + 150 z - 500 z^2 + 1250 z^3 + 3125 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(97656250 (1 - z)^(31/5) 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