z^(Subscript[a, 1] Subscript[a, 2]) == (z^Subscript[a, 1])^Subscript[a, 2] Exp[-2 I Pi Subscript[a, 2] k] /; Inequality[-Pi - 2 Pi k, Less, Im[Subscript[a, 1] Log[z]], LessEqual, Pi - 2 Pi k] && Element[k, Integers]

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List[SubscriptBox["a", "1"], " ", SubscriptBox["a", "2"]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", SubscriptBox["a", "1"]], ")"]], SubscriptBox["a", "2"]], RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", SubscriptBox["a", "2"], " ", "k"]], "]"]]]]]], " ", "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "-", RowBox[List["2", "\[Pi]", " ", "k"]]]], "<", RowBox[List["Im", "[", RowBox[List[SubscriptBox["a", "1"], " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", RowBox[List["\[Pi]", "-", RowBox[List["2", "\[Pi]", " ", "k"]]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </msup> <mo> ) </mo> </mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <pi /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <ci> k </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 /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </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>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", RowBox[List[SubscriptBox["a_", "1"], " ", SubscriptBox["a_", "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", SubscriptBox["aa", "1"]], ")"]], SubscriptBox["aa", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", SubscriptBox["aa", "2"], " ", "k"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "-", RowBox[List["2", " ", "\[Pi]", " ", "k"]]]], "<", RowBox[List["Im", "[", RowBox[List[SubscriptBox["aa", "1"], " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", RowBox[List["\[Pi]", "-", RowBox[List["2", " ", "\[Pi]", " ", "k"]]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]]]

2007-05-02