## Lucas Polynomial Sequence

A pair of generalized Polynomials which generalize the Lucas Sequence to Polynomials is given by

 (1) (2)

where
 (3)

 (4)

 (5)

(Horadam 1996). Setting gives
 (6) (7)

giving
 (8) (9)

The sequences most commonly considered have , giving
 (10) (11)

Special cases are given in the following table.

 Polynomial 1 Polynomial 2 1 Fibonacci Lucas 1 Pell Pell-Lucas 1 Jacobsthal Jacobsthal Fermat Fermat-Lucas Chebyshev Polynomial of the Second Kind Chebyshev Polynomial of the First Kind

Horadam, A. F. Extension of a Synthesis for a Class of Polynomial Sequences.'' Fib. Quart. 34, 68-74, 1996.