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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Continued fraction representations





http://functions.wolfram.com/01.03.10.0003.01









  


  








Input Form





E^z == 1 + z/(1 - z/(2 + z/(3 - z/(2 + z/(5 - z/(2 + z/(7 - \[Ellipsis])))))))








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List["1", "+", FractionBox["z", RowBox[List["1", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["3", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["5", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["7", "-", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> - </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> - </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#8230; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox["z", RowBox[List["1", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["3", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["5", "-", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["7", "-", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]


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





2001-10-29