Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
NorlundB




Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α] > Summation > Finite summation





http://functions.wolfram.com/05.16.23.0002.01









  


  








Input Form





Sum[Binomial[n - z, n + k] Binomial[n + z, n - k] Binomial[n + k - 1, n] NorlundB[n, k + n], {k, 0, n}] == (-1)^n Binomial[z, n] NorlundB[n, n - z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "-", "z"]], ",", RowBox[List["n", "+", "k"]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "+", "z"]], ",", RowBox[List["n", "-", "k"]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "+", "k", "-", "1"]], ",", "n"]], "]"]], " ", RowBox[List["NorlundB", "[", RowBox[List["n", ",", RowBox[List["k", "+", "n"]]]], "]"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Binomial", "[", RowBox[List["z", ",", "n"]], "]"]], " ", RowBox[List["NorlundB", "[", RowBox[List["n", ",", RowBox[List["n", "-", "z"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> - </mo> <mi> z </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;z&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List[&quot;k&quot;, &quot;+&quot;, &quot;n&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <mi> z </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;z&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;k&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;k&quot;, &quot;+&quot;, &quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[&quot;n&quot;, Identity, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> &#8290; </mo> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> z </mi> </mtd> </mtr> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;z&quot;, Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[&quot;n&quot;, Identity, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> &#8290; </mo> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox[&quot;B&quot;, NorlundB] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> k </ci> <ci> n </ci> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> n </ci> <ci> z </ci> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> k </ci> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> n </ci> </apply> <apply> <ci> NorlundB </ci> <ci> n </ci> <apply> <plus /> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Binomial </ci> <ci> z </ci> <ci> n </ci> </apply> <apply> <ci> NorlundB </ci> <ci> n </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n_", "-", "z_"]], ",", RowBox[List["n_", "+", "k_"]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n_", "+", "z_"]], ",", RowBox[List["n_", "-", "k_"]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n_", "+", "k_", "-", "1"]], ",", "n_"]], "]"]], " ", RowBox[List["NorlundB", "[", RowBox[List["n_", ",", RowBox[List["k_", "+", "n_"]]]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Binomial", "[", RowBox[List["z", ",", "n"]], "]"]], " ", RowBox[List["NorlundB", "[", RowBox[List["n", ",", RowBox[List["n", "-", "z"]]]], "]"]]]]]]]]


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





2007-05-02