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Tanh




Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/01.21.06.0023.01









  


  








Input Form





Tanh[z] \[Proportional] z - z^3/3 + (2 z^5)/15 - O[z^7]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Tanh", "[", "z", "]"]], "\[Proportional]", RowBox[List["z", "-", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", "5"]]], "15"], "-", RowBox[List["O", "[", SuperscriptBox["z", "7"], "]"]]]]]]]]








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> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mn> 15 </mn> </mfrac> <mo> - </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <tanh /> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 15 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", "-", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", "5"]]], "15"], "-", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "7"]]]]]]]


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





2007-05-02