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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > General characteristics > Symmetries and periodicities > Scale symmetry





http://functions.wolfram.com/01.02.04.0007.01









  


  








Input Form





(z^a)^b == z^(a b) /; Inequality[-Pi, Less, Im[a Log[z]], LessEqual, Pi] || Inequality[-1, Less, a, LessEqual, 1] || Element[b, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "a"], ")"]], "b"], "\[Equal]", SuperscriptBox["z", RowBox[List["a", " ", "b"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]], "\[Or]", RowBox[List[RowBox[List["-", "1"]], "<", "a", "\[LessEqual]", "1"]], "\[Or]", RowBox[List["b", "\[Element]", "Integers"]]]]]]]]








MathML Form







<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> z </mi> <mi> a </mi> </msup> <mo> ) </mo> </mrow> <mi> b </mi> </msup> <mo> &#10869; </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <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> <mi> &#960; </mi> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> a </mi> <mo> &#8804; </mo> <mn> 1 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mi> b </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 /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <or /> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <leq /> <pi /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> -1 </cn> <lt /> <ci> a </ci> <leq /> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> b </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["z_", "a_"], ")"]], "b_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List["a", " ", "b"]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]], "||", RowBox[List[RowBox[List["-", "1"]], "<", "a", "\[LessEqual]", "1"]], "||", RowBox[List["b", "\[Element]", "Integers"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29