Coth[z] == (E^z + E^(-z))/(E^z - E^(-z))

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<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> &#10869; </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> + </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> - </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]], RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]]]]]]]

2001-10-29