Pell-Lucas Polynomial

Author

Eric W. Weisstein
March 24, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/Pell-LucasPolynomial.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Pell-LucasPolynomial.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Plot

<<Graphics`Colors`

Plot[Evaluate[Table[PellQ[n,x],{n,0,5}]],{x,-1,1},
PlotStyle->{Black,Red,Yellow,Green,Blue,Violet},
AxesLabel->TraditionalForm/@{x,Subscript[Q,n][x]}]

Enumeration

Table[PellQ[n,x],{n,0,5}]//Simplify//Expand//ColumnForm//TraditionalForm

Relation to PellP

Q_n(x)=P_{n-1}(x)+P_{n+1}(x).

Subtract@@@Table[{PellQ[n,x],PellP[n-1,x]+PellP[n+1,x]},{n,6}]//Simplify