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http://functions.wolfram.com/05.14.17.0001.01
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BernoulliB[n, z] == BernoulliB[n, z + 1] - n z^(n - 1)
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Cell[BoxData[RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["n", ",", RowBox[List["z", "+", "1"]]]], "]"]], "-", RowBox[List["n", " ", SuperscriptBox["z", RowBox[List["n", "-", "1"]]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BernoulliB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BernoulliB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BernoulliB </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> BernoulliB </ci> <ci> n </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> n </ci> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BernoulliB", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["n", ",", RowBox[List["z", "+", "1"]]]], "]"]], "-", RowBox[List["n", " ", SuperscriptBox["z", RowBox[List["n", "-", "1"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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