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 BernoulliB

 http://functions.wolfram.com/04.13.23.0017.01

 Input Form

 Sum[(BernoulliB[n]/n!) z^n, {n, 0, Infinity}] == z/(E^z - 1) /; Abs[z] < 2 Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["BernoulliB", "[", "n", "]"]], RowBox[List["n", "!"]]], " ", SuperscriptBox["z", "n"]]]]], "\[Equal]", FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", RowBox[List["2", " ", "\[Pi]"]]]]]]]]

 MathML Form

 n = 0 B TagBox["B", BernoulliB] n z n n ! z z - 1 /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 2 π Condition n 0 BernoulliB n z n n -1 z z -1 -1 z 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n_", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["BernoulliB", "[", "n_", "]"]], " ", SuperscriptBox["z_", "n_"]]], RowBox[List["n_", "!"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", RowBox[List["2", " ", "\[Pi]"]]]]]]]]]]

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

 2001-10-29