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 Log

 http://functions.wolfram.com/01.04.08.0001.01

 Input Form

 Log[z] == ((z - 1)/(E - 1)) Product[(E^2^(-k) + 1)/(z^2^(-k) + 1), {k, 1, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["\[ExponentialE]", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["2", RowBox[List["-", "k"]]]], "+", "1"]], RowBox[List[SuperscriptBox["z", SuperscriptBox["2", RowBox[List["-", "k"]]]], "+", "1"]]]]]]]]]]]

 MathML Form

 log ( z ) z - 1 - 1 k = 1 2 - k + 1 z 2 - k + 1 z z -1 -1 -1 k 1 2 -1 k 1 z 2 -1 k 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["2", RowBox[List["-", "k"]]]], "+", "1"]], RowBox[List[SuperscriptBox["z", SuperscriptBox["2", RowBox[List["-", "k"]]]], "+", "1"]]]]]]], RowBox[List["\[ExponentialE]", "-", "1"]]]]]]]

 Contributed by

 Ruffa Anthony

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

 2003-08-21