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Exp




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.03.26.0076.01









  


  








Input Form





E^z == Sqrt[(z Pi)/2] (BesselI[1/2, z] + BesselI[-(1/2), z])








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List[SqrtBox[FractionBox[RowBox[List["z", " ", "\[Pi]"]], "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "2"], ",", "z"]], "]"]], "+", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], ")"]]]]]]]]








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> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> I </mi> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <ci> z </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <ci> BesselI </ci> <cn type='rational'> 1 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[FractionBox[RowBox[List["z", " ", "\[Pi]"]], "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "2"], ",", "z"]], "]"]], "+", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], ")"]]]]]]]]


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





2001-10-29