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http://functions.wolfram.com/01.03.26.0077.01
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E^z == (-I) Sqrt[(Pi I z)/2] BesselY[-(1/2), I z] -
Sqrt[-((Pi I z)/2)] BesselY[1/2, (-I) z]
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "z"]], "2"]], " ", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "z"]], "2"]]]], " ", RowBox[List["BesselY", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "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> ⅇ </mi> <mi> z </mi> </msup> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msqrt> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> Y </mi> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <mrow> <msub> <mi> Y </mi> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> BesselY </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <pi /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselY </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "z"]], "2"]], " ", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "z"]], ")"]]]]], " ", RowBox[List["BesselY", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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