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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=-22/5, b>=a > For fixed z and a=-22/5, b=4





http://functions.wolfram.com/07.23.03.aqi0.01









  


  










Input Form





Hypergeometric2F1[-(22/5), 4, 3/5, -z] == (1/390625) (390625 + 10419860 z + 48206730 z^2 + 72974880 z^3 + 34871760 z^4 + 5236 z^(2/5) (119 + 1496 z + 5049 z^2 + 6336 z^3 + 2664 z^4) Log[1 + z^(1/5)] + 5236 (-1)^(2/5) z^(2/5) (119 + 1496 z + 5049 z^2 + 6336 z^3 + 2664 z^4) Log[1 - (-1)^(1/5) z^(1/5)] + 623084 (-1)^(4/5) z^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] + 7833056 (-1)^(4/5) z^(7/5) Log[1 + (-1)^(2/5) z^(1/5)] + 26436564 (-1)^(4/5) z^(12/5) Log[1 + (-1)^(2/5) z^(1/5)] + 33175296 (-1)^(4/5) z^(17/5) Log[1 + (-1)^(2/5) z^(1/5)] + 13948704 (-1)^(4/5) z^(22/5) Log[1 + (-1)^(2/5) z^(1/5)] - 623084 (-1)^(1/5) z^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - 7833056 (-1)^(1/5) z^(7/5) Log[1 - (-1)^(3/5) z^(1/5)] - 26436564 (-1)^(1/5) z^(12/5) Log[1 - (-1)^(3/5) z^(1/5)] - 33175296 (-1)^(1/5) z^(17/5) Log[1 - (-1)^(3/5) z^(1/5)] - 13948704 (-1)^(1/5) z^(22/5) Log[1 - (-1)^(3/5) z^(1/5)] - 623084 (-1)^(3/5) z^(2/5) Log[1 + (-1)^(4/5) z^(1/5)] - 7833056 (-1)^(3/5) z^(7/5) Log[1 + (-1)^(4/5) z^(1/5)] - 26436564 (-1)^(3/5) z^(12/5) Log[1 + (-1)^(4/5) z^(1/5)] - 33175296 (-1)^(3/5) z^(17/5) Log[1 + (-1)^(4/5) z^(1/5)] - 13948704 (-1)^(3/5) z^(22/5) Log[1 + (-1)^(4/5) z^(1/5)])










Standard Form





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MathML Form







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&#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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7833056 </mn> <mo> &#8290; </mo> <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> <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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10419860 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 5236 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2664 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6336 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5049 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1496 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 119 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 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<mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 623084 </mn> <mo> &#8290; </mo> <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> <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> 2 </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> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 623084 </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> 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<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='rational'> 7 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7833056 </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'> 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='rational'> 7 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10419860 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 5236 </cn> <apply> <plus /> 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<apply> <times /> <cn type='integer'> 623084 </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'> 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='rational'> 2 <sep /> 5 </cn> </apply> </apply> </apply> <cn type='integer'> 390625 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










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





2007-05-02