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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Transformations > Products, sums, and powers of the direct function > Powers of the direct function





http://functions.wolfram.com/01.03.16.0096.01









  


  








Input Form





(E^z)^a == E^(a z) Exp[2 I Pi a Floor[(Pi - Im[z])/(2 Pi)]]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", "z"], ")"]], "a"], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", RowBox[List["Exp", "[", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "a", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", "z", "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mi> a </mi> </msup> <mo> &#10869; </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> exp </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <ci> a </ci> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <ci> z </ci> </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>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", "z_"], ")"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "a", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", "z", "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]]


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





2001-10-29