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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=3, b>=a > For fixed z and a=3, b=6





http://functions.wolfram.com/07.23.03.b2nq.01









  


  








Input Form





Hypergeometric2F1[3, 6, -(6/5), z] == (1/(390625 (-1 + z)^10)) (390625 - 9765625 z + 486328125 z^2 + 2236152637 z^3 + 1461593690 z^4 + 42296100 z^5 - 3426500 z^6 + 192500 z^7) - (1/(1953125 (1 - z)^(51/5))) (2234232 Sqrt[2 (5 + Sqrt[5])] z^(11/5) (168 + 525 z + 250 z^2) 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/(1953125 (1 - z)^(51/5))) (2234232 Sqrt[10 - 2 Sqrt[5]] z^(11/5) (168 + 525 z + 250 z^2) 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))]) - (4468464 z^(11/5) (168 + 525 z + 250 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(51/5)) - (1117116 (-1 + Sqrt[5]) z^(11/5) (168 + 525 z + 250 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(51/5)) + (1117116 (1 + Sqrt[5]) z^(11/5) (168 + 525 z + 250 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(51/5))








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