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Sech




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.24.06.0001.02









  


  








Input Form





Sech[z] \[Proportional] 1 - z^2/2 + (5 z^4)/24 - (61 z^6)/720 + \[Ellipsis] /; (z -> 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sech", "[", "z", "]"]], "\[Proportional]", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "2"], "2"], "+", FractionBox[RowBox[List["5", " ", SuperscriptBox["z", "4"]]], "24"], "-", FractionBox[RowBox[List["61", " ", SuperscriptBox["z", "6"]]], "720"], "+", "\[Ellipsis]"]]]], "/;", " ", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 24 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 61 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mn> 720 </mn> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> </mrow> <mo> /; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 24 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 61 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mn> 720 </mn> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> </mrow> <mo> /; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sech", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "2"], "2"], "+", FractionBox[RowBox[List["5", " ", SuperscriptBox["z", "4"]]], "24"], "-", FractionBox[RowBox[List["61", " ", SuperscriptBox["z", "6"]]], "720"], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]


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





2001-10-29