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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.b3kj.01









  


  








Input Form





Hypergeometric2F1[4, 5, -(29/5), z] == (1/(86093750 (-1 + z)^14)) (86093750 - 1502187500 z + 12918515625 z^2 - 74760000000 z^3 + 343607578125 z^4 - 1494238593750 z^5 + 9058400859375 z^6 + 41060826266172 z^7 + 25090058449815 z^8 + 2941313531050 z^9 + 16408642250 z^10) - (1/(390625 (1 - z)^(74/5))) (6432426 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (7007 + 10780 z + 3675 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)^(74/5))) (6432426 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (7007 + 10780 z + 3675 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))]) + (12864852 z^(34/5) (7007 + 10780 z + 3675 z^2 + 250 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(74/5)) + (1/(390625 (1 - z)^(74/5))) (3216213 (-1 + Sqrt[5]) z^(34/5) (7007 + 10780 z + 3675 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)^(74/5))) (3216213 (1 + Sqrt[5]) z^(34/5) (7007 + 10780 z + 3675 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