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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Continued fraction representations





http://functions.wolfram.com/01.03.10.0005.01









  


  








Input Form





E^Sqrt[z] == 1 + (2 Sqrt[z])/(2 - Sqrt[z] + z/ (3 (2 + z/(15 (2 + z/(35 (2 + z/(63 (2 + z/(99 (2 + \[Ellipsis])))))))))\ ))








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", SqrtBox["z"]], "\[Equal]", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["2", "-", SqrtBox["z"], "+", FractionBox[RowBox[List["z", "/", "3"]], RowBox[List[" ", RowBox[List["2", "+", FractionBox[RowBox[List["z", "/", "15"]], RowBox[List[" ", RowBox[List["2", "+", FractionBox[RowBox[List["z", "/", "35"]], RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["z", "/", "63"]], " "]], RowBox[List["2", "+", FractionBox[RowBox[List["z", "/", "99"]], RowBox[List["2", "+", "\[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> <msqrt> <mi> z </mi> </msqrt> </msup> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> / </mo> <mn> 3 </mn> </mrow> <mrow> <mtext> </mtext> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> / </mo> <mn> 15 </mn> </mrow> <mrow> <mtext> </mtext> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> / </mo> <mn> 35 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mrow> <mi> z </mi> <mo> / </mo> <mn> 63 </mn> </mrow> <mtext> </mtext> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> / </mo> <mn> 99 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 15 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 35 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 63 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 99 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </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]", SqrtBox["z_"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["2", "-", SqrtBox["z"], "+", FractionBox["z", RowBox[List["3", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox["z", RowBox[List["15", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox["z", RowBox[List["35", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox["z", RowBox[List["63", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox["z", RowBox[List["99", " ", RowBox[List["(", RowBox[List["2", "+", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]]]]]]]]]


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





2001-10-29