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variants of this functions
NorlundB






Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α] > Series representations > Generalized power series > Expansions at generic point z==z0





http://functions.wolfram.com/05.16.06.0001.01









  


  










Input Form





NorlundB[n, z] \[Proportional] NorlundB[n, Subscript[z, 0]] + Derivative[0, 1][NorlundB][n, Subscript[z, 0]] (z - Subscript[z, 0]) + (1/2) Derivative[0, 2][NorlundB][n, Subscript[z, 0]] (z - Subscript[z, 0])^2 + \[Ellipsis] /; (z -> Subscript[z, 0])










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msubsup> <mo> &#8733; </mo> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </msubsup> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <semantics> <msubsup> <mi> B </mi> <mi> n </mi> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msubsup> <annotation encoding='Mathematica'> TagBox[SubsuperscriptBox[TagBox[&quot;B&quot;, NorlundB], &quot;n&quot;, RowBox[List[&quot;(&quot;, &quot;z&quot;, &quot;)&quot;]]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <mrow> <mo> &#8706; 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</ms> <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> &#8706; </ms> <ms> z </ms> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> | </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> &#10869; </ms> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 0 </ms> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <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> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 2 </ms> </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> &#8706; </ms> <ms> 2 </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> &#8706; </ms> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> | </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> &#10869; </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> 2 </ms> </apply> </list> </apply> <ms> + </ms> <ms> &#8230; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], "+", RowBox[List[RowBox[List[SuperscriptBox["NorlundB", TagBox[RowBox[List["(", RowBox[List["0", ",", "1"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SuperscriptBox["NorlundB", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["zz", "0"]]], ")"]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





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