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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=-24/5, b>=a > For fixed z and a=-24/5, b=4





http://functions.wolfram.com/07.23.03.apo7.01









  


  








Input Form





Hypergeometric2F1[-(24/5), 4, 1/5, z] == (1/390625) (390625 - 18395880 z + 96281740 z^2 - 154742840 z^3 + 76715730 z^4 + 9576 z^(4/5) (399 - 4256 z + 13224 z^2 - 15776 z^3 + 6409 z^4) Log[1 - z^(1/5)] + 9576 (-1)^(4/5) z^(4/5) (399 - 4256 z + 13224 z^2 - 15776 z^3 + 6409 z^4) Log[1 + (-1)^(1/5) z^(1/5)] - 3820824 (-1)^(3/5) z^(4/5) Log[1 - (-1)^(2/5) z^(1/5)] + 40755456 (-1)^(3/5) z^(9/5) Log[1 - (-1)^(2/5) z^(1/5)] - 126633024 (-1)^(3/5) z^(14/5) Log[1 - (-1)^(2/5) z^(1/5)] + 151070976 (-1)^(3/5) z^(19/5) Log[1 - (-1)^(2/5) z^(1/5)] - 61372584 (-1)^(3/5) z^(24/5) Log[1 - (-1)^(2/5) z^(1/5)] + 3820824 (-1)^(2/5) z^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] - 40755456 (-1)^(2/5) z^(9/5) Log[1 + (-1)^(3/5) z^(1/5)] + 126633024 (-1)^(2/5) z^(14/5) Log[1 + (-1)^(3/5) z^(1/5)] - 151070976 (-1)^(2/5) z^(19/5) Log[1 + (-1)^(3/5) z^(1/5)] + 61372584 (-1)^(2/5) z^(24/5) Log[1 + (-1)^(3/5) z^(1/5)] - 3820824 (-1)^(1/5) z^(4/5) Log[1 - (-1)^(4/5) z^(1/5)] + 40755456 (-1)^(1/5) z^(9/5) Log[1 - (-1)^(4/5) z^(1/5)] - 126633024 (-1)^(1/5) z^(14/5) Log[1 - (-1)^(4/5) z^(1/5)] + 151070976 (-1)^(1/5) z^(19/5) Log[1 - (-1)^(4/5) z^(1/5)] - 61372584 (-1)^(1/5) z^(24/5) Log[1 - (-1)^(4/5) z^(1/5)])








Standard Form





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MathML Form







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<mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <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> 3 </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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40755456 </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> 9 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 18395880 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 9576 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6409 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15776 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13224 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4256 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 399 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> 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Rule Form





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





2007-05-02