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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.aoij.01









  


  










Input Form





Hypergeometric2F1[-(28/5), 5, -(8/5), z] == (1/390625) (6279 (-(3533750/6279) - 625/(-1 + z) + (831875 z)/1794 + (1904375 z^2)/78 - (9543985 z^3)/26 + 988570 z^4 - 718960 z^5 - 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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z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 63756 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 1904375 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> 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</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'> 2 <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'> 23 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 754908 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 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<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> <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 /> <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> <cn type='integer'> 1 </cn> </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 </cn> </apply> <apply> 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<cn type='integer'> 5719 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3059 </cn> <ci> z </ci> </apply> <cn type='integer'> -483 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3268 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5719 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3059 </cn> <ci> z </ci> </apply> <cn type='integer'> -483 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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'> 13 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 63756 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> 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</math>










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





2007-05-02