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 Log

 http://functions.wolfram.com/01.04.16.0101.01

 Input Form

 Log[(-1)^r z^r] == I Pi r + r Log[z] /; Inequality[0, Less, r, LessEqual, 1/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r"], " ", SuperscriptBox["z", "r"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "r"]], "+", RowBox[List["r", " ", RowBox[List["Log", "[", "z", "]"]]]]]]]], "/;", RowBox[List["0", "<", "r", "\[LessEqual]", FractionBox["1", "2"]]]]]]]

 MathML Form

 log ( ( - 1 ) r z r ) log ( z ) r + π r /; 0 < r 1 2 Condition -1 r z r z r r Inequality 0 r 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r_"], " ", SuperscriptBox["z_", "r_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "r"]], "+", RowBox[List["r", " ", RowBox[List["Log", "[", "z", "]"]]]]]], "/;", RowBox[List["0", "<", "r", "\[LessEqual]", FractionBox["1", "2"]]]]]]]]]

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

 2007-05-02