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

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<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> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mi> &#960; </mi> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <msub> <mi> K </mi> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </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 /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselK </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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

2001-10-29