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 Log

 http://functions.wolfram.com/01.04.06.0038.01

 Input Form

 Log[1 + z] \[Proportional] Log[z] + 1/z - 1/(2 z^2) + 1/(3 z^3) + O[1/z^4]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", FractionBox["1", "z"], "-", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox["1", RowBox[List["3", " ", SuperscriptBox["z", "3"]]]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "4"]], "]"]]]]]]]]

 MathML Form

 log ( 1 + z ) log ( z ) + 1 z - 1 2 z 2 + 1 3 z 3 + O ( 1 z 4 ) Proportional 1 z z 1 z -1 -1 1 2 z 2 -1 1 3 z 3 -1 O 1 z 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["1", "+", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", FractionBox["1", "z"], "-", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox["1", RowBox[List["3", " ", SuperscriptBox["z", "3"]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "4"]], "]"]]]]]]]]

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

 2007-05-02