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 BernoulliB

 http://functions.wolfram.com/04.13.23.0004.01

 Input Form

 Sum[Binomial[n, k] BernoulliB[k] z^k, {k, 0, n}] == z^n BernoulliB[n, 1/z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", RowBox[List["BernoulliB", "[", "k", "]"]], " ", SuperscriptBox["z", "k"]]]]], "\[Equal]", RowBox[List[SuperscriptBox["z", "n"], RowBox[List["BernoulliB", "[", RowBox[List["n", ",", FractionBox["1", "z"]]], "]"]]]]]]]]

 MathML Form

 k = 0 n ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] B TagBox["B", BernoulliB] k z k z n B TagBox["B", BernoulliB] n ( 1 z ) k 0 n Binomial n k BernoulliB k z k z n BernoulliB n 1 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n_", ",", "k_"]], "]"]], " ", RowBox[List["BernoulliB", "[", "k_", "]"]], " ", SuperscriptBox["z_", "k_"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "n"], " ", RowBox[List["BernoulliB", "[", RowBox[List["n", ",", FractionBox["1", "z"]]], "]"]]]]]]]]

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

 2001-10-29