## Pell and Pell-Lucas polynomials.(English)Zbl 0557.10011

Pell polynomials $$P_ n(x)$$ and Pell-Lucas polynomials $$Q_ n(x)$$ are defined by the recurrence relations $$P_{n+2}(x)=2\times P_{n+1}(x)+P_ n(x)$$, $$P_ 0(x)=0$$, $$P_ 1(x)=1$$ and $$Q_{n+2}(x)=2\times Q_{n+1}(x)+Q_ n(x)$$, $$Q_ 0(x)=2$$, $$Q_ 1(x)=2$$, respectively. Basic properties of these polynomials are established by a variety of means, one of the most fruitful being the use of matrices. The relationships of $$P_ n(x)$$ and $$Q_ n(x)$$ to some classical polynomials, such as the Gegenbauer polynomial and the Chebyshev polynomials, are briefly investigated.

### MSC:

 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B37 Recurrences