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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Representations through equivalent functions > With related functions > Involving tanh





http://functions.wolfram.com/01.20.27.0041.01









  


  








Input Form





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








Standard Form





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








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










Rule Form





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


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





2001-10-29