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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=-9/5, b>=a > For fixed z and a=-9/5, b=2





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









  


  








Input Form





Hypergeometric2F1[-(9/5), 2, 11/5, -z] == (1/(3125 z^(6/5))) (180 z^(1/5) + 935 z^(6/5) + 630 z^(11/5) + 36 (1 + z)^2 (-1 + 14 z) Log[1 + z^(1/5)] + 36 (-1)^(4/5) (1 + z)^2 (-1 + 14 z) Log[1 - (-1)^(1/5) z^(1/5)] + 36 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] - 432 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] - 972 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 504 (-1)^(3/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 36 (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] + 432 (-1)^(2/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 972 (-1)^(2/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 504 (-1)^(2/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] + 36 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 432 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 972 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 504 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)])








Standard Form





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MathML Form







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<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> 3 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 5 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <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> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ 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type='integer'> 935 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 6 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 432 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 432 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 432 </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'> 4 <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> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 180 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> 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Rule Form





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





2007-05-02