Pell Polynomial

Author

Eric W. Weisstein
January 20, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/PellPolynomial.nb.

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

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

Plot

Plot[Evaluate[Table[PellP[n,x],{n,0,5}]],{x,-1,1},
PlotStyle->{Black,Red,Yellow,Green,Blue,Purple},
AxesLabel->{x,Subscript[P,n][x]}]

Enumeration

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

Table[Fibonacci[n,2x],{n,0,5}]//ColumnForm//TraditionalForm

Table[CoefficientList[Fibonacci[n,2x],x],{n,0,5}]

Table[CoefficientList[ChebyshevU[n-1,x],x],{n,0,5}]

Flatten[%]