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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.b47v.01









  


  








Input Form





Hypergeometric2F1[5, 5, -(19/5), z] == -((1/(155859375 (-1 + z)^13)) (155859375 - 3051562500 z + 32078906250 z^2 - 270064062500 z^3 + 2892738281250 z^4 + 26269365893924 z^5 + 31895948828750 z^6 + 8998904607300 z^7 + 445466824375 z^8)) - (1/(1953125 (1 - z)^(69/5))) (845988 Sqrt[2 (5 + Sqrt[5])] z^(24/5) (70499 + 194480 z + 128700 z^2 + 22000 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)^(69/5))) (845988 Sqrt[10 - 2 Sqrt[5]] z^(24/5) (70499 + 194480 z + 128700 z^2 + 22000 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))]) + (1691976 z^(24/5) (70499 + 194480 z + 128700 z^2 + 22000 z^3 + 625 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(69/5)) + (1/(1953125 (1 - z)^(69/5))) (422994 (-1 + Sqrt[5]) z^(24/5) (70499 + 194480 z + 128700 z^2 + 22000 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)^(69/5))) (422994 (1 + Sqrt[5]) z^(24/5) (70499 + 194480 z + 128700 z^2 + 22000 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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type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 24 <sep /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02