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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Representations through more general functions > Through other functions





http://functions.wolfram.com/01.02.26.0046.01









  


  








Input Form





z^(1/n) == Root[Function[x, x^n - z], n] /; n == 2 || (Element[n - 3, Integers] && n - 3 >= 0 && !IntervalMemberQ[Interval[{0, Infinity}], z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "n"]]], "\[Equal]", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["x", ",", RowBox[List[SuperscriptBox["x", "n"], "-", "z"]]]], "]"]], ",", "n"]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Equal]", "2"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["n", "-", "3"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["n", "-", "3"]], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "\[Infinity]"]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]], ")"]]]]]]]]








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> <mn> 1 </mn> <mo> / </mo> <mi> n </mi> </mrow> </msup> <mo> &#10869; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> x </mi> <mo> ; </mo> <mrow> <msup> <mi> x </mi> <mi> n </mi> </msup> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#10869; </mo> <mn> 2 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mtext> &#8203; </mtext> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> n </mi> </mrow> </msup> <mo> &#10869; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> x </mi> <mo> ; </mo> <mrow> <msup> <mi> x </mi> <mi> n </mi> </msup> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#10869; </mo> <mn> 2 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mtext> &#8203; </mtext> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", FractionBox["1", "n_"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["x", ",", RowBox[List[SuperscriptBox["x", "n"], "-", "z"]]]], "]"]], ",", "n"]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Equal]", "2"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["n", "-", "3"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["n", "-", "3"]], "\[GreaterEqual]", "0"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]]]


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





2001-10-29