ArcTan[-Infinity, y] == (2 UnitStep[Re[y]] - 1) Pi

Cell[BoxData[RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["-", " ", "\[Infinity]"]], ",", "y"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", RowBox[List["UnitStep", "[", RowBox[List["Re", "[", "y", "]"]], "]"]]]], "-", "1"]], ")"]], "\[Pi]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> &#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arctan /> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> <ci> y </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> &#952; </ci> <apply> <real /> <ci> y </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "y_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["UnitStep", "[", RowBox[List["Re", "[", "y", "]"]], "]"]]]], "-", "1"]], ")"]], " ", "\[Pi]"]]]]]]

2001-10-29