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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Transformations > Half-angle formulas > With respect to a





http://functions.wolfram.com/01.02.16.0077.01









  


  








Input Form





z^(a/2) == (z^a)^(1/2) /; Inequality[-Pi, Less, Im[a Log[z]], LessEqual, Pi]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["z", FractionBox["a", "2"]], "\[Equal]", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "a"], ")"]], FractionBox["1", "2"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]]]]]]








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> <mi> z </mi> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#10869; </mo> <msqrt> <msup> <mi> z </mi> <mi> a </mi> </msup> </msqrt> </mrow> <mo> /; </mo> <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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <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> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", FractionBox["a_", "2"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[SuperscriptBox["z", "a"]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]


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





2007-05-02