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http://functions.wolfram.com/02.13.19.0007.01
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Arg[DirectedInfinity[E^(I x)]] == x + 2 Pi Floor[(Pi - x)/(2 Pi)] /;
Element[x, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Arg", "[", RowBox[List["DirectedInfinity", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "x"]]], "]"]], "]"]], "\[Equal]", RowBox[List["x", "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", "x"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]], "/;", " ", RowBox[List["x", "\[Element]", "Reals"]]]]]]
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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> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> x </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arg /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> x </ci> </apply> </apply> <infinity /> </apply> </apply> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", RowBox[List["DirectedInfinity", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "x_"]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", "x"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
