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variants of this functions
NorlundB




Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α,z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/05.17.06.0005.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", "\[Alpha]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", "\[Alpha]"]], "]"]], "+", RowBox[List["n", " ", RowBox[List["NorlundB", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "\[Alpha]"]], "]"]], "z"]], "+", RowBox[List[FractionBox[RowBox[List["n", RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]]]], "2"], RowBox[List["NorlundB", "[", RowBox[List[RowBox[List["n", "-", "2"]], ",", "\[Alpha]"]], "]"]], SuperscriptBox["z", "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <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> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> + </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mrow> <mo> ( </mo> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> NorlundB </ci> <ci> n </ci> <ci> &#945; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> NorlundB </ci> <ci> n </ci> <ci> &#945; </ci> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> NorlundB </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> &#945; </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <ci> n </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> NorlundB </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> <ci> &#945; </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["n_", ",", "\[Alpha]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", "\[Alpha]"]], "]"]], "+", RowBox[List["n", " ", RowBox[List["NorlundB", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "\[Alpha]"]], "]"]], " ", "z"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["n", " ", RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]]]], ")"]], " ", RowBox[List["NorlundB", "[", RowBox[List[RowBox[List["n", "-", "2"]], ",", "\[Alpha]"]], "]"]], " ", SuperscriptBox["z", "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]


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





2007-05-02