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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.b4c7.01









  


  








Input Form





Hypergeometric2F1[5, 6, 21/5, z] == (88 (198 - 1635 z + 7650 z^2 + 27250 z^3 + 1250 z^4))/ (9765625 (-1 + z)^6 z^3) - (792 Sqrt[2 (5 + Sqrt[5])] (-11 + 100 z - 500 z^2 + 5000 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)^(34/5) z^(16/5)) - (792 Sqrt[10 - 2 Sqrt[5]] (-11 + 100 z - 500 z^2 + 5000 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)^(34/5) z^(16/5)) + (1584 (-11 + 100 z - 500 z^2 + 5000 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(48828125 (1 - z)^(34/5) z^(16/5)) + (396 (-1 + Sqrt[5]) (-11 + 100 z - 500 z^2 + 5000 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)])/(48828125 (1 - z)^(34/5) z^(16/5)) - (396 (1 + Sqrt[5]) (-11 + 100 z - 500 z^2 + 5000 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)])/(48828125 (1 - z)^(34/5) z^(16/5))








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