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 Log

 http://functions.wolfram.com/01.04.27.0013.01

 Input Form

 Log[z] == 2 I ArcTan[(I (1 - z))/(1 + z)] + 2 Pi I /; z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]], RowBox[List["1", "+", "z"]]], "]"]]]], "+", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]]]]], " ", "/;", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]

 MathML Form

 log ( z ) 2 tan - 1 ( ( 1 - z ) z + 1 ) + 2 π /; z < - 1 Condition z 2 1 -1 z z 1 -1 2 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]], RowBox[List["1", "+", "z"]]], "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]

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

 2001-10-29