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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Transformations > Half-angle formulas





http://functions.wolfram.com/01.22.16.0038.01









  


  








Input Form





Coth[z/2] == z Sqrt[1/z^2] Sqrt[(Cosh[z] + 1)/(Cosh[z] - 1)]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox["z", "2"], "]"]], "\[Equal]", RowBox[List["z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "+", "1"]], RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", "1"]]]]]]]]]]








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> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox["z_", "2"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "+", "1"]], RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", "1"]]]]]]]]]]


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





2001-10-29