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 ProductLog

 http://functions.wolfram.com/01.32.04.0017.01

 Input Form

 Limit[ProductLog[1, x - I \[Epsilon]], \[Epsilon] -> Plus[0]] == ProductLog[x] /; x < -(1/E)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["ProductLog", "[", RowBox[List["1", ",", RowBox[List["x", "-", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]"]]]]]], "]"]], ",", RowBox[List["\[Epsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Equal]", RowBox[List["ProductLog", "[", "x", "]"]]]], "/;", RowBox[List["x", "<", RowBox[List["-", FractionBox["1", "\[ExponentialE]"]]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["ProductLog", "[", RowBox[List["1", ",", RowBox[List["x_", "-", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]]]], "]"]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductLog", "[", "x", "]"]], "/;", RowBox[List["x", "<", RowBox[List["-", FractionBox["1", "\[ExponentialE]"]]]]]]]]]]]

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

 2001-10-29