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 Log

 http://functions.wolfram.com/01.04.16.0081.01

 Input Form

 Log[Sqrt[z^2]] == Log[z] + Pi I /; Inequality[-Pi, Less, Arg[z], LessEqual, -(Pi/2)]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", SqrtBox[SuperscriptBox["z", "2"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", SqrtBox[SuperscriptBox["z_", "2"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]]]

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

 2007-05-02