Norlund polynomials: Specific values (formula 05.17.03.0013)

NorlundB

$Mathematica Notation$

http://functions.wolfram.com/05.17.03.0013.01

Input Form

NorlundB[7, \[Alpha], z] == (1/1152) (1152 z^7 - 4032 z^6 \[Alpha] - 5040 z^4 (-1 + \[Alpha]) \[Alpha]^2 + 2016 z^5 \[Alpha] (-1 + 3 \[Alpha]) - 252 z^2 \[Alpha]^2 (2 + 5 \[Alpha] - 10 \[Alpha]^2 + 3 \[Alpha]^3) + 168 z^3 \[Alpha] (2 + 5 \[Alpha] - 30 \[Alpha]^2 + 15 \[Alpha]^3) + \[Alpha]^2 (16 + 42 \[Alpha] - 7 \[Alpha]^2 - 105 \[Alpha]^3 + 63 \[Alpha]^4 - 9 \[Alpha]^5) + 2 z \[Alpha] (-16 - 42 \[Alpha] + 91 \[Alpha]^2 + 315 \[Alpha]^3 - 315 \[Alpha]^4 + 63 \[Alpha]^5))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["7", ",", "\[Alpha]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1152"], RowBox[List["(", RowBox[List[RowBox[List["1152", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["4032", " ", SuperscriptBox["z", "6"], " ", "\[Alpha]"]], "-", RowBox[List["5040", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Alpha]"]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["2016", " ", SuperscriptBox["z", "5"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "\[Alpha]"]]]], ")"]]]], "-", RowBox[List["252", " ", SuperscriptBox["z", "2"], " ", 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["168", " ", SuperscriptBox["z", "3"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["30", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[Alpha]", "2"], " ", RowBox[List["(", RowBox[List["16", "+", RowBox[List["42", " ", "\[Alpha]"]], "-", RowBox[List["7", " ", SuperscriptBox["\[Alpha]", "2"]]], "-", RowBox[List["105", " ", SuperscriptBox["\[Alpha]", "3"]]], "+", RowBox[List["63", " ", SuperscriptBox["\[Alpha]", "4"]]], "-", RowBox[List["9", " ", SuperscriptBox["\[Alpha]", "5"]]]]], ")"]]]], "+", RowBox[List["2", " ", "z", " ", "\[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"]]]]], ")"]]]]]], ")"]]]]]]]]

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["B", NorlundB] </annotation> </semantics> <mn> 7 </mn> <mrow> <mo> ( </mo> <mi> α </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 1152 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1152 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4032 </mn> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2016 </mn> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5040 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> α </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 168 </mn> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 252 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 63 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 91 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 42 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> - </mo> <mn> 16 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <msup> <mi> α </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 63 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 105 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 42 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> + </mo> <mn> 16 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> NorlundB </ci> <cn type='integer'> 7 </cn> <ci> α </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1152 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1152 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4032 </cn> <ci> α </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2016 </cn> <ci> α </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> α </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5040 </cn> <apply> <plus /> <ci> α </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 168 </cn> <ci> α </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> α </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> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> α </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 252 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> α </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> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> α </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <power /> <ci> α </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> α </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 42 </cn> <ci> α </ci> </apply> </apply> <cn type='integer'> -16 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -9 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 42 </cn> <ci> α </ci> </apply> <cn type='integer'> 16 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["7", ",", "\[Alpha]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["1152", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["4032", " ", SuperscriptBox["z", "6"], " ", "\[Alpha]"]], "-", RowBox[List["5040", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Alpha]"]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["2016", " ", SuperscriptBox["z", "5"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "\[Alpha]"]]]], ")"]]]], "-", RowBox[List["252", " ", SuperscriptBox["z", "2"], " ", 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["168", " ", SuperscriptBox["z", "3"], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "\[Alpha]"]], "-", RowBox[List["30", " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Alpha]", "3"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[Alpha]", "2"], " ", RowBox[List["(", RowBox[List["16", "+", RowBox[List["42", " ", "\[Alpha]"]], "-", RowBox[List["7", " ", SuperscriptBox["\[Alpha]", "2"]]], "-", RowBox[List["105", " ", SuperscriptBox["\[Alpha]", "3"]]], "+", RowBox[List["63", " ", SuperscriptBox["\[Alpha]", "4"]]], "-", RowBox[List["9", " ", SuperscriptBox["\[Alpha]", "5"]]]]], ")"]]]], "+", RowBox[List["2", " ", "z", " ", "\[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"]]]]], ")"]]]]]], "1152"]]]]]

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

2007-05-02

NorlundB[n,z]