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http://functions.wolfram.com/01.02.16.0076.01
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z^(a/2) == (z^a)^(1/2) /; Element[a, Reals] &&
Inequality[-Pi, Less, a Arg[z], LessEqual, Pi]
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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["a", "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["a", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]]
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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> <mi> z </mi> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⩵ </mo> <msqrt> <msup> <mi> z </mi> <mi> a </mi> </msup> </msqrt> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> a </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mo> - </mo> <mi> π </mi> </mrow> <mo> < </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ≤ </mo> <mi> π </mi> </mrow> </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> <and /> <apply> <in /> <ci> a </ci> <reals /> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <times /> <ci> a </ci> <apply> <arg /> <ci> z </ci> </apply> </apply> <leq /> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", FractionBox["a_", "2"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[SuperscriptBox["z", "a"]], "/;", RowBox[List[RowBox[List["a", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["a", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
