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http://functions.wolfram.com/04.13.09.0001.01
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BernoulliB[n] == Limit[D[z/(E^z - 1), {z, n}], z -> 0]
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Cell[BoxData[RowBox[List[RowBox[List["BernoulliB", "[", "n", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "n"]], "}"]]], FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]], ",", RowBox[List["z", "\[Rule]", "0"]]]], "]"]]]]]]
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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> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BernoulliB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ⩵ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> n </mi> </msup> <mfrac> <mi> z </mi> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BernoulliB </ci> <ci> n </ci> </apply> <apply> <limit /> <bvar> <ci> z </ci> </bvar> <condition> <apply> <tendsto /> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BernoulliB", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "n"]], "}"]]]]], FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]], ",", RowBox[List["z", "\[Rule]", "0"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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