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http://functions.wolfram.com/05.16.06.0002.01
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NorlundB[n, z] == NorlundB[n, Subscript[z, 0]] +
Sum[(1/k!) Derivative[0, k][NorlundB][n, Subscript[z, 0]]
(z - Subscript[z, 0])^k, {k, 1, n}]
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Cell[BoxData[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", SubscriptBox["z", "0"]]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List[FractionBox["1", RowBox[List["k", "!"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List["0", ",", "k"]], "]"]], "[", "NorlundB", "]"]], "[", RowBox[List["n", ",", SubscriptBox["z", "0"]]], "]"]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "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> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msubsup> <mo>  </mo> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </msubsup> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> k </mi> </msup> <semantics> <msubsup> <mi> B </mi> <mi> n </mi> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msubsup> <annotation encoding='Mathematica'> TagBox[SubsuperscriptBox[TagBox["B", NorlundB], "n", RowBox[List["(", "z", ")"]]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> </mfrac> <msub> <mo> | </mo> <mrow> <mi> z </mi> <mo> ⩵ </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> NorlundB </ci> </apply> <ms> n </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> </apply> <ms>  </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> NorlundB </ci> </apply> <ms> n </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 0 </ms> </apply> <ms> ) </ms> </list> </apply> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∑ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> n </ms> </apply> <apply> <ci> ErrorBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> ! </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> ∂ </ms> <ms> k </ms> </apply> <apply> <ci> TagBox </ci> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> NorlundB </ci> </apply> <ms> n </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <ci> $CellContext`e </ci> <apply> <ci> Zeta </ci> <ci> $CellContext`e </ci> </apply> </apply> </apply> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> k </ms> </apply> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> | </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> ⩵ </ms> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 0 </ms> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 0 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> k </ms> </apply> </list> </apply> </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["NorlundB", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["NorlundB", TagBox[RowBox[List["(", RowBox[List["0", ",", "k"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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