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http://functions.wolfram.com/05.14.32.0001.01
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Element[q^n (BernoulliB[n, p/q] - BernoulliB[n, 0]), Integers] /;
Element[n, Integers] && n > 0 && Element[p, Integers] &&
Element[q, Integers] && q != 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["q", "n"], " ", RowBox[List["(", RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["n", ",", FractionBox["p", "q"]]], "]"]], "-", RowBox[List["BernoulliB", "[", RowBox[List["n", ",", "0"]], "]"]]]], ")"]]]], "\[Element]", "Integers"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List["q", "\[Element]", "Integers"]], "\[And]", RowBox[List["q", "\[NotEqual]", "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> <mrow> <mrow> <msup> <mi> q </mi> <mi> n </mi> </msup> <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> <mfrac> <mi> p </mi> <mi> q </mi> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BernoulliB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mi> p </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> q </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> q </mi> <mo> ≠ </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <in /> <apply> <times /> <apply> <power /> <ci> q </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <ci> BernoulliB </ci> <ci> n </ci> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> q </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> BernoulliB </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <integers /> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <in /> <ci> p </ci> <integers /> </apply> <apply> <in /> <ci> q </ci> <integers /> </apply> <apply> <neq /> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["q", "n"], " ", RowBox[List["(", RowBox[List[RowBox[List["BernoulliB", "[", RowBox[List["n", ",", FractionBox["p", "q"]]], "]"]], "-", RowBox[List["BernoulliB", "[", RowBox[List["n", ",", "0"]], "]"]]]], ")"]]]], "\[Element]", "Integers"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List["q", "\[Element]", "Integers"]], "&&", RowBox[List["q", "\[NotEqual]", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
