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http://functions.wolfram.com/01.03.16.0092.01
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E^(Subscript[z, 1] Subscript[z, 2]) == (E^Subscript[z, 1])^Subscript[z, 2]
Exp[-2 I Pi Subscript[z, 2] Floor[(Pi - Im[Subscript[z, 1]])/(2 Pi)]]
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SubscriptBox["z", "1"], " ", SubscriptBox["z", "2"]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", SubscriptBox["z", "1"]], ")"]], SubscriptBox["z", "2"]], " ", RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", SubscriptBox["z", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", SubscriptBox["z", "1"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "]"]]]]]]]]
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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> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </msup> <mo> ) </mo> </mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </msup> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <pi /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List[SubscriptBox["z_", "1"], " ", SubscriptBox["z_", "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", SubscriptBox["zz", "1"]], ")"]], SubscriptBox["zz", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", SubscriptBox["zz", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", SubscriptBox["zz", "1"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
