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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Continued fraction representations





http://functions.wolfram.com/01.28.10.0001.01









  


  










Input Form





ArcCoth[z] == 1/ (z (1 - 1/(z^2 (3 - 4/(z^2 (5 - 9/(z^2 (7 - 16/(z^2 (9 - 25/(z^2 (11 - 36/(z^2 (13 - \[Ellipsis])))))))))))))) /; !IntervalMemberQ[Interval[{-1, 1}], z]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 9 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 25 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 11 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 13 </mn> <mo> - </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> <mo> /; </mo> <mtext> &#8203; </mtext> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 9 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 25 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 11 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 13 </mn> <mo> - </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> <mo> /; </mo> <mtext> &#8203; </mtext> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29