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Pell-Lucas Polynomial

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Pell-LucasPolynomial

The Pell-Lucas polynomials Q(x) are the w-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. The first few are

Q_1(x)=2x
(1)
Q_2(x)=4x^2+2
(2)
Q_3(x)=8x^3+6x
(3)
Q_4(x)=16x^4+16x^2+2
(4)
Q_5(x)=32x^5+40x^3+10x.
(5)

They are related to the Pell polynomials P_n(x) by

Q_n(x)=P_(n-1)(x)+P_(n+1)(x).
(6)

See also

Lucas Polynomial Sequence, Pell-Lucas Number, Pell Number, Pell Polynomial

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Cite this as:

Weisstein, Eric W. "Pell-Lucas Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Pell-LucasPolynomial.html

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