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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=5





http://functions.wolfram.com/07.23.03.b48i.01









  


  








Input Form





Hypergeometric2F1[5, 5, 9/5, z] == (7 (166581 + 919025 z + 747575 z^2 + 81875 z^3))/(1171875 (-1 + z)^8) - (1/(1953125 (1 - z)^(41/5) z^(4/5))) (88 Sqrt[2 (5 + Sqrt[5])] (44 + 3520 z + 13200 z^2 + 8000 z^3 + 625 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/(1953125 (1 - z)^(41/5) z^(4/5))) (88 Sqrt[10 - 2 Sqrt[5]] (44 + 3520 z + 13200 z^2 + 8000 z^3 + 625 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))]) - (176 (44 + 3520 z + 13200 z^2 + 8000 z^3 + 625 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(41/5) z^(4/5)) - (44 (-1 + Sqrt[5]) (44 + 3520 z + 13200 z^2 + 8000 z^3 + 625 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(41/5) z^(4/5)) + (44 (1 + Sqrt[5]) (44 + 3520 z + 13200 z^2 + 8000 z^3 + 625 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(41/5) z^(4/5))








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