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http://functions.wolfram.com/01.02.16.0101.01
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(E^z)^a == E^(a (z + 2 I Pi k)) /;
Inequality[-Pi - 2 Pi k, Less, Im[z], LessEqual, Pi - 2 Pi k] &&
Element[k, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", "z"], ")"]], "a"], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "k"]]]], ")"]]]]]]], " ", "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "-", RowBox[List["2", "\[Pi]", " ", "k"]]]], "<", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", RowBox[List["\[Pi]", "-", RowBox[List["2", "\[Pi]", " ", "k"]]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]
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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> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mi> a </mi> </msup> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> π </mi> </mrow> <mo> < </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <ci> a </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <ci> k </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Inequality </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <pi /> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> <lt /> <apply> <imaginary /> <ci> z </ci> </apply> <leq /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", "z_"], ")"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "k"]]]], ")"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "-", RowBox[List["2", " ", "\[Pi]", " ", "k"]]]], "<", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", RowBox[List["\[Pi]", "-", RowBox[List["2", " ", "\[Pi]", " ", "k"]]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
