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 Log

 http://functions.wolfram.com/01.05.06.0017.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["a_", ",", RowBox[List["1", "+", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", "-", FractionBox[SuperscriptBox["z", "2"], "2"], "+", FractionBox[SuperscriptBox["z", "3"], "3"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]], RowBox[List["Log", "[", "a", "]"]]]]]]]

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

 2007-05-02