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

Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List["Cosh", "[", "z", "]"]], RowBox[List["Sinh", "[", "z", "]"]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]], RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]]]]]]]

<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> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <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> <cosh /> <ci> z </ci> </apply> <apply> <power /> <apply> <sinh /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </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["Coth", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List["Cosh", "[", "z", "]"]], RowBox[List["Sinh", "[", "z", "]"]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]], RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]]]]]]]

2001-10-29