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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=-19/5, b>=a > For fixed z and a=-19/5, b=4





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









  


  








Input Form





Hypergeometric2F1[-(19/5), 4, 1/5, z] == (1/234375) (234375 - 8260440 z + 29081780 z^2 - 23604840 z^3 - 4788 z^(4/5) (-399 + 3192 z - 6612 z^2 + 3944 z^3) Log[1 - z^(1/5)] - 4788 (-1)^(4/5) z^(4/5) (-399 + 3192 z - 6612 z^2 + 3944 z^3) Log[1 + (-1)^(1/5) z^(1/5)] - 1910412 (-1)^(3/5) z^(4/5) Log[1 - (-1)^(2/5) z^(1/5)] + 15283296 (-1)^(3/5) z^(9/5) Log[1 - (-1)^(2/5) z^(1/5)] - 31658256 (-1)^(3/5) z^(14/5) Log[1 - (-1)^(2/5) z^(1/5)] + 18883872 (-1)^(3/5) z^(19/5) Log[1 - (-1)^(2/5) z^(1/5)] + 1910412 (-1)^(2/5) z^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] - 15283296 (-1)^(2/5) z^(9/5) Log[1 + (-1)^(3/5) z^(1/5)] + 31658256 (-1)^(2/5) z^(14/5) Log[1 + (-1)^(3/5) z^(1/5)] - 18883872 (-1)^(2/5) z^(19/5) Log[1 + (-1)^(3/5) z^(1/5)] - 1910412 (-1)^(1/5) z^(4/5) Log[1 - (-1)^(4/5) z^(1/5)] + 15283296 (-1)^(1/5) z^(9/5) Log[1 - (-1)^(4/5) z^(1/5)] - 31658256 (-1)^(1/5) z^(14/5) Log[1 - (-1)^(4/5) z^(1/5)] + 18883872 (-1)^(1/5) z^(19/5) Log[1 - (-1)^(4/5) z^(1/5)])








Standard Form





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MathML Form







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</mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1910412 </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> <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> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mn> 234375 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 19 <sep 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Rule Form





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





2007-05-02