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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Representations through more general functions > Through other functions > Involving Jacobi functions





http://functions.wolfram.com/01.03.26.0084.01









  


  








Input Form





E^z == 1/JacobiDN[z, 1] + I/JacobiDN[(Pi I)/2 - z, 1]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "1"]], "]"]]], "+", FractionBox["\[ImaginaryI]", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", "z"]], ",", "1"]], "]"]]]]]]]]]








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> <mfrac> <mn> 1 </mn> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> z </mi> </mrow> <mo> &#10072; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <ci> JacobiDN </ci> <apply> <plus /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </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[FractionBox["1", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "1"]], "]"]]], "+", FractionBox["\[ImaginaryI]", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", "z"]], ",", "1"]], "]"]]]]]]]]]


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





2001-10-29