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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/05.17.03.0010.01









  


  








Input Form





NorlundB[4, \[Alpha], z] == z^4 - 2 z^3 \[Alpha] - (1/2) z (-1 + \[Alpha]) \[Alpha]^2 + (1/2) z^2 \[Alpha] (-1 + 3 \[Alpha]) + (1/240) \[Alpha] (2 + 5 \[Alpha] - 30 \[Alpha]^2 + 15 \[Alpha]^3)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["4", ",", "\[Alpha]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["z", "4"], "-", RowBox[List["2", " ", SuperscriptBox["z", "3"], " ", "\[Alpha]"]], "-", RowBox[List[FractionBox["1", "2"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Alpha]"]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", "2"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "\[Alpha]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "240"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["30", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]]]]]]]]








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> 4 </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> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </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> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </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> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 240 </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> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> NorlundB </ci> <cn type='integer'> 4 </cn> <ci> &#945; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#945; </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </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'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <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> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 240 </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> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["4", ",", "\[Alpha]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "4"], "-", RowBox[List["2", " ", SuperscriptBox["z", "3"], " ", "\[Alpha]"]], "-", RowBox[List[FractionBox["1", "2"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Alpha]"]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", "2"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "\[Alpha]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "240"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["30", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]]]]]]]]


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





2007-05-02