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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=4, b>=a > For fixed z and a=4, b=5





http://functions.wolfram.com/07.23.03.b3l6.01









  


  








Input Form





Hypergeometric2F1[4, 5, -(1/5), z] == (-78125 + 8515625 z + 69659679 z^2 + 86540495 z^3 + 18453850 z^4 + 115500 z^5)/(78125 (-1 + z)^9) + (1/(390625 (1 - z)^(46/5))) (24024 Sqrt[2 (5 + Sqrt[5])] z^(6/5) (308 + 1680 z + 1575 z^2 + 250 z^3) 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/(390625 (1 - z)^(46/5))) (24024 Sqrt[10 - 2 Sqrt[5]] z^(6/5) (308 + 1680 z + 1575 z^2 + 250 z^3) 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))]) + (48048 z^(6/5) (308 + 1680 z + 1575 z^2 + 250 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(46/5)) + (1/(390625 (1 - z)^(46/5))) (12012 (-1 + Sqrt[5]) z^(6/5) (308 + 1680 z + 1575 z^2 + 250 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(390625 (1 - z)^(46/5))) (12012 (1 + Sqrt[5]) z^(6/5) (308 + 1680 z + 1575 z^2 + 250 z^3) 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