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http://functions.wolfram.com/04.13.06.0009.01
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BernoulliB[2 n] == Subscript[A, n] - DivisorSum[1/Subscript[p, k],
{Subscript[p, k] - 1, 2 n}] /; Element[Subscript[A, n], Integers] &&
Subscript[p, k] == Prime[k]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["2", "n"]], "]"]], "\[Equal]", RowBox[List[SubscriptBox["A", "n"], "-", RowBox[List["DivisorSum", "[", RowBox[List[FractionBox["1", SubscriptBox["p", "k"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["p", "k"], "-", "1"]], ",", RowBox[List["2", "n"]]]], "}"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["A", "n"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["p", "k"], "\[Equal]", RowBox[List["Prime", "[", "k", "]"]]]]]]]]]]
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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> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msub> <mo> ⩵ </mo> <mrow> <msub> <mi> A </mi> <mi> n </mi> </msub> <mo> - </mo> <mstyle scriptlevel='0'> <mrow> <munder> <mo> ∑ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> p </mi> <mi> k </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> | </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </munder> <mfrac> <mn> 1 </mn> <msub> <mi> p </mi> <mi> k </mi> </msub> </mfrac> </mrow> </mstyle> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> A </mi> <mi> n </mi> </msub> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> p </mi> <mi> k </mi> </msub> <mo> ⩵ </mo> <mrow> <mi> prime </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> BernoulliB </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> n </ms> </list> </apply> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> A </ms> <ms> n </ms> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> ∑ </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> p </ms> <ms> k </ms> </apply> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> | </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> n </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </apply> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> SubscriptBox </ci> <ms> p </ms> <ms> k </ms> </apply> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> A </ms> <ms> n </ms> </apply> <ms> ∈ </ms> <apply> <ci> TagBox </ci> <ms> ℤ </ms> <apply> <ci> Function </ci> <list /> <integers /> </apply> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> p </ms> <ms> k </ms> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <ms> prime </ms> <ms> ( </ms> <ms> k </ms> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BernoulliB", "[", RowBox[List["2", " ", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["A", "n"], "-", RowBox[List["DivisorSum", "[", RowBox[List[FractionBox["1", SubscriptBox["p", "k"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["p", "k"], "-", "1"]], ",", RowBox[List["2", " ", "n"]]]], "}"]]]], "]"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["A", "n"], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["p", "k"], "\[Equal]", RowBox[List["Prime", "[", "k", "]"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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