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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.b4bn.01









  


  








Input Form





Hypergeometric2F1[5, 6, -(4/5), z] == (1/(19531250 (-1 + z)^11)) (-19531250 + 947265625 z + 31355890348 z^2 + 103374363490 z^3 + 75996940150 z^4 + 11547092875 z^5 + 86782500 z^6) + (1/(48828125 (1 - z)^(59/5))) (1180242 Sqrt[2 (5 + Sqrt[5])] z^(9/5) (7714 + 55100 z + 87000 z^2 + 36250 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))]) + (1/(48828125 (1 - z)^(59/5))) (1180242 Sqrt[10 - 2 Sqrt[5]] z^(9/5) (7714 + 55100 z + 87000 z^2 + 36250 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))]) - (2360484 z^(9/5) (7714 + 55100 z + 87000 z^2 + 36250 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(48828125 (1 - z)^(59/5)) - (1/(48828125 (1 - z)^(59/5))) (590121 (-1 + Sqrt[5]) z^(9/5) (7714 + 55100 z + 87000 z^2 + 36250 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)]) + (1/(48828125 (1 - z)^(59/5))) (590121 (1 + Sqrt[5]) z^(9/5) (7714 + 55100 z + 87000 z^2 + 36250 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)])








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