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 Log

 http://functions.wolfram.com/01.04.27.0043.01

 Input Form

 Log[z] == 2 ArcCoth[(z + 1)/(z - 1)] + Pi I (1 - Sqrt[z + 1] Sqrt[1/(z + 1)])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcCoth", "[", FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["z", "+", "1"]]], " ", SqrtBox[FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]], ")"]]]]]]]]]]

 MathML Form

 log ( z ) 2 coth - 1 ( z + 1 z - 1 ) + π ( 1 - z + 1 1 z + 1 ) z 2 z 1 z -1 -1 1 -1 z 1 1 2 1 z 1 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcCoth", "[", FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["z", "+", "1"]]], " ", SqrtBox[FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]], ")"]]]]]]]]]]

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

 2001-10-29