Norlund polynomials: Specific values (formula 05.17.03.0014)

NorlundB

$Mathematica Notation$

http://functions.wolfram.com/05.17.03.0014.01

Input Form

NorlundB[8, \[Alpha], z] == z^8 - 4 z^7 \[Alpha] - 7 z^5 (-1 + \[Alpha]) \[Alpha]^2 + (7/3) z^6 \[Alpha] (-1 + 3 \[Alpha]) - (7/12) z^3 \[Alpha]^2 (2 + 5 \[Alpha] - 10 \[Alpha]^2 + 3 \[Alpha]^3) + (7/24) z^4 \[Alpha] (2 + 5 \[Alpha] - 30 \[Alpha]^2 + 15 \[Alpha]^3) - (1/144) z \[Alpha]^2 (-16 - 42 \[Alpha] + 7 \[Alpha]^2 + 105 \[Alpha]^3 - 63 \[Alpha]^4 + 9 \[Alpha]^5) + (1/144) z^2 \[Alpha] (-16 - 42 \[Alpha] + 91 \[Alpha]^2 + 315 \[Alpha]^3 - 315 \[Alpha]^4 + 63 \[Alpha]^5) + (\[Alpha] (144 + 404 \[Alpha] - 540 \[Alpha]^2 - 2345 \[Alpha]^3 - 840 \[Alpha]^4 + 3150 \[Alpha]^5 - 1260 \[Alpha]^6 + 135 \[Alpha]^7))/34560

Standard Form

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MathML Form

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</mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 24 </mn> </mfrac> <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> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 12 </mn> </mfrac> <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> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 144 </mn> </mfrac> <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> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 144 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> 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</mo> <mrow> <mn> 2345 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 540 </mn> <mo> ⁢ </mo> <msup> <mi> α </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 404 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> + </mo> <mn> 144 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 34560 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> NorlundB </ci> <cn type='integer'> 8 </cn> <ci> α </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> α </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 3 </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'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </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'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 24 </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'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 7 <sep /> 12 </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'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 144 </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> <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 /> 144 </cn> <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'> -1 </cn> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </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> <apply> <times /> <ci> α </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 135 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1260 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3150 </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'> 840 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2345 </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'> 540 </cn> <apply> <power /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 404 </cn> <ci> α </ci> </apply> <cn type='integer'> 144 </cn> </apply> <apply> <power /> <cn type='integer'> 34560 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02

NorlundB[n,z]