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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Continued fraction representations





http://functions.wolfram.com/01.22.10.0003.01









  


  








Input Form





Coth[z] == 1/z + z/(3 + z^2/(5 + z^2/(7 + z^2/(9 + z^2/(11 + \[Ellipsis])))))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "z"], "+", FractionBox[RowBox[List[" ", "z"]], RowBox[List["3", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["5", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["7", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["9", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["11", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> + </mo> <mfrac> <mrow> <mtext> </mtext> <mi> z </mi> </mrow> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 7 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 9 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 11 </mn> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 11 </cn> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "z"], "+", FractionBox["z", RowBox[List["3", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["5", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["7", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["9", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["11", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]










Contributed by





Andreas Lauschke (2006)


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





2007-05-02