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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.b482.01









  


  








Input Form





Hypergeometric2F1[5, 5, -(11/5), z] == -((1/(4296875 (-1 + z)^12)) (-4296875 + 100390625 z - 1601953125 z^2 + 72771484375 z^3 + 388944182501 z^4 + 423788197425 z^5 + 113618815075 z^6 + 5258429375 z^7)) + (1/(1953125 (1 - z)^(61/5))) (203112 Sqrt[2 (5 + Sqrt[5])] z^(16/5) (25389 + 96720 z + 83700 z^2 + 18000 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)^(61/5))) (203112 Sqrt[10 - 2 Sqrt[5]] z^(16/5) (25389 + 96720 z + 83700 z^2 + 18000 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))]) + (406224 z^(16/5) (25389 + 96720 z + 83700 z^2 + 18000 z^3 + 625 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (1953125 (1 - z)^(61/5)) + (1/(1953125 (1 - z)^(61/5))) (101556 (-1 + Sqrt[5]) z^(16/5) (25389 + 96720 z + 83700 z^2 + 18000 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)]) - (1/(1953125 (1 - z)^(61/5))) (101556 (1 + Sqrt[5]) z^(16/5) (25389 + 96720 z + 83700 z^2 + 18000 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)])








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