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variants of this functions
NorlundB






Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α,z] > Specific values > Specialized values > For fixed alpha, z





http://functions.wolfram.com/05.17.03.0012.01









  


  










Input Form





NorlundB[6, \[Alpha], z] == z^6 - 3 z^5 \[Alpha] - (5/2) z^3 (-1 + \[Alpha]) \[Alpha]^2 + (5/4) z^4 \[Alpha] (-1 + 3 \[Alpha]) - (1/16) z \[Alpha]^2 (2 + 5 \[Alpha] - 10 \[Alpha]^2 + 3 \[Alpha]^3) + (1/16) z^2 \[Alpha] (2 + 5 \[Alpha] - 30 \[Alpha]^2 + 15 \[Alpha]^3) + (\[Alpha] (-16 - 42 \[Alpha] + 91 \[Alpha]^2 + 315 \[Alpha]^3 - 315 \[Alpha]^4 + 63 \[Alpha]^5))/4032










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> <mn> 6 </mn> <mrow> <mo> ( </mo> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> z </mi> <mn> 6 </mn> </msup> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 30 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 63 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 91 </mn> <mo> &#8290; </mo> <msup> <mi> &#945; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 42 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> - </mo> <mn> 16 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4032 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> NorlundB </ci> <cn type='integer'> 6 </cn> <ci> &#945; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#945; </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 5 <sep /> 4 </cn> <ci> &#945; </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#945; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 5 <sep /> 2 </cn> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <ci> &#945; </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> &#945; </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> &#945; </ci> </apply> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> &#945; </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 42 </cn> <ci> &#945; </ci> </apply> </apply> <cn type='integer'> -16 </cn> </apply> <apply> <power /> <cn type='integer'> 4032 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["6", ",", "\[Alpha]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "6"], "-", RowBox[List["3", " ", SuperscriptBox["z", "5"], " ", "\[Alpha]"]], "-", RowBox[List[FractionBox["5", "2"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Alpha]"]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[FractionBox["5", "4"], " ", SuperscriptBox["z", "4"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "\[Alpha]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "16"], " ", "z", " ", SuperscriptBox["\[Alpha]", "2"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["10", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["z", "2"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["30", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]], "+", FractionBox[RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["42", " ", "\[Alpha]"]], "+", RowBox[List["91", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["315", " ", SuperscriptBox["\[Alpha]", "3"]]], "-", RowBox[List["315", " ", SuperscriptBox["\[Alpha]", "4"]]], "+", RowBox[List["63", " ", SuperscriptBox["\[Alpha]", "5"]]]]], ")"]]]], "4032"]]]]]]]










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





2007-05-02





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