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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=2/5, b>=a > For fixed z and a=2/5, b=1





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









  


  










Input Form





Hypergeometric2F1[2/5, 1, 22/5, -z] == (1/(1875 z^(17/5))) (17 (-1)^(1/5) (210 (-1)^(4/5) z^(2/5) + 570 (-1)^(4/5) z^(7/5) + 485 (-1)^(4/5) z^(12/5) + 84 (-1)^(4/5) (1 + z)^3 Log[1 + z^(1/5)] + 84 (-1)^(2/5) (1 + z)^3 Log[1 - (-1)^(1/5) z^(1/5)] + 84 Log[1 + (-1)^(2/5) z^(1/5)] + 252 z Log[1 + (-1)^(2/5) z^(1/5)] + 252 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 84 z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 84 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 252 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 252 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 84 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 84 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 252 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 252 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 84 (-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> / </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> 84 </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> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 2 <sep /> 5 </cn> <cn type='integer'> 1 </cn> </list> <list> <cn type='rational'> 22 <sep /> 5 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> 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<cn type='rational'> 3 <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='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </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> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> 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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 252 </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'> 210 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ln /> <apply> 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Rule Form





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





2007-05-02