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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=-28/5, b>=a > For fixed z and a=-28/5, b=5





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









  


  








Input Form





Hypergeometric2F1[-(28/5), 5, -(8/5), -z] == (1/390625) (6279 (-(3533750/6279) - (831875 z)/1794 + (1904375 z^2)/78 + (9543985 z^3)/26 + 988570 z^4 + 718960 z^5 + 625/(1 + z) - 132 z^(13/5) (483 + 3059 z + 5719 z^2 + 3268 z^3) Log[1 + z^(1/5)] + 132 (-1)^(3/5) z^(13/5) (483 + 3059 z + 5719 z^2 + 3268 z^3) Log[1 - (-1)^(1/5) z^(1/5)] + 63756 (-1)^(1/5) z^(13/5) Log[1 + (-1)^(2/5) z^(1/5)] + 403788 (-1)^(1/5) z^(18/5) Log[1 + (-1)^(2/5) z^(1/5)] + 754908 (-1)^(1/5) z^(23/5) Log[1 + (-1)^(2/5) z^(1/5)] + 431376 (-1)^(1/5) z^(28/5) Log[1 + (-1)^(2/5) z^(1/5)] - 63756 (-1)^(4/5) z^(13/5) Log[1 - (-1)^(3/5) z^(1/5)] - 403788 (-1)^(4/5) z^(18/5) Log[1 - (-1)^(3/5) z^(1/5)] - 754908 (-1)^(4/5) z^(23/5) Log[1 - (-1)^(3/5) z^(1/5)] - 431376 (-1)^(4/5) z^(28/5) Log[1 - (-1)^(3/5) z^(1/5)] - 63756 (-1)^(2/5) z^(13/5) Log[1 + (-1)^(4/5) z^(1/5)] - 403788 (-1)^(2/5) z^(18/5) Log[1 + (-1)^(4/5) z^(1/5)] - 754908 (-1)^(2/5) z^(23/5) Log[1 + (-1)^(4/5) z^(1/5)] - 431376 (-1)^(2/5) z^(28/5) Log[1 + (-1)^(4/5) z^(1/5)]))








Standard Form





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MathML Form







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<times /> <cn type='integer'> 431376 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 28 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 431376 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> 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<cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 403788 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 403788 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 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Date Added to functions.wolfram.com (modification date)





2007-05-02