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 Log

 http://functions.wolfram.com/01.04.04.0014.01

 Input Form

 Limit[Log[x + I \[Epsilon]], \[Epsilon] -> Plus[0]] == Log[-x] + Pi I /; x < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]"]]]], "]"]], ",", RowBox[List["\[Epsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Equal]", " ", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", " ", RowBox[List["x", "<", "0"]]]]]]

 MathML Form

 lim ϵ "\[Rule]" + 0 log ( x + ϵ ) log ( - x ) + π /; x < 0 Condition ϵ ϵ 0 x ϵ -1 x x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]], "]"]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List["x", "<", "0"]]]]]]]]

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

 2007-05-02