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Sqrt




Mathematica Notation

Traditional Notation









Elementary Functions > Sqrt[z] > Transformations > Some functions of arguments





http://functions.wolfram.com/01.01.16.0082.01









  


  








Input Form





Sqrt[x^Subscript[a, 1] y^Subscript[a, 2] z^Subscript[a, 3]] == E^(I Pi Floor[(Pi - Im[Subscript[a, 1] Log[x]] - Im[Subscript[a, 2] Log[y]] - Im[Subscript[a, 3] Log[z]])/(2 Pi)]) x^(Subscript[a, 1]/2) y^(Subscript[a, 2]/2) z^(Subscript[a, 3]/2)








Standard Form





Cell[BoxData[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["x", SubscriptBox["a", "1"]], SuperscriptBox["y", SubscriptBox["a", "2"]], " ", SuperscriptBox["z", SubscriptBox["a", "3"]]]]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["a", "1"], " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["a", "2"], " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["a", "3"], " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], SuperscriptBox["x", RowBox[List[SubscriptBox["a", "1"], "/", "2"]]], " ", SuperscriptBox["y", RowBox[List[SubscriptBox["a", "2"], "/", "2"]]], SuperscriptBox["z", RowBox[List[SubscriptBox["a", "3"], "/", "2"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msqrt> <mrow> <msup> <mi> x </mi> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </msup> <mo> &#8290; </mo> <msup> <mi> y </mi> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </msup> </mrow> </msqrt> <mo> &#63449; </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> x </mi> <mfrac> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mn> 2 </mn> </mfrac> </msup> <mo> &#8290; </mo> <msup> <mi> y </mi> <mfrac> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mn> 2 </mn> </mfrac> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mfrac> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mn> 2 </mn> </mfrac> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <power /> <ci> x </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> y </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ln /> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </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> <power /> <ci> x </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> y </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[RowBox[List[SuperscriptBox["x_", SubscriptBox["a_", "1"]], " ", SuperscriptBox["y_", SubscriptBox["a_", "2"]], " ", SuperscriptBox["z_", SubscriptBox["a_", "3"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["aa", "1"], " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["aa", "2"], " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List[SubscriptBox["aa", "3"], " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SuperscriptBox["x", FractionBox[SubscriptBox["aa", "1"], "2"]], " ", SuperscriptBox["y", FractionBox[SubscriptBox["aa", "2"], "2"]], " ", SuperscriptBox["z", FractionBox[SubscriptBox["aa", "3"], "2"]]]]]]]]


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





2007-05-02