|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/12.02.16.0022.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Arg[x^a] == Im[a] Log[x] /; Inequality[-(Pi/Log[x]), Less, Im[a], LessEqual,
Pi/Log[x]] && Element[x, Reals] && x > 0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Arg", "[", SuperscriptBox["x", "a"], "]"]], "\[Equal]", RowBox[List[RowBox[List["Im", "[", "a", "]"]], RowBox[List["Log", "[", "x", "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", RowBox[List["Log", "[", "x", "]"]]]]], "<", RowBox[List["Im", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", RowBox[List["Log", "[", "x", "]"]]]]], "\[And]", RowBox[List["x", "\[Element]", TagBox["Reals", Function[Reals]]]], "\[And]", RowBox[List["x", ">", "0"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> x </mi> <mi> a </mi> </msup> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> π </mi> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> < </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mfrac> <mi> π </mi> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> x </mi> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arg /> <apply> <power /> <ci> x </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <imaginary /> <ci> a </ci> </apply> <apply> <ln /> <ci> x </ci> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <apply> <ln /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <lt /> <apply> <imaginary /> <ci> a </ci> </apply> <leq /> <apply> <times /> <pi /> <apply> <power /> <apply> <ln /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", SuperscriptBox["x_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", "x", "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", RowBox[List["Log", "[", "x", "]"]]]]], "<", RowBox[List["Im", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", RowBox[List["Log", "[", "x", "]"]]]]], "&&", RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", ">", "0"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
