## Fibonacci Polynomial

The Polynomials obtained by setting and in the Lucas Polynomial Sequence. (The corresponding Polynomials are called Lucas Polynomials.) The Fibonacci polynomials are defined by the Recurrence Relation

 (1)

with and . They are also given by the explicit sum formula
 (2)

where is the Floor Function and is a Binomial Coefficient. The first few Fibonacci polynomials are

The Fibonacci polynomials are normalized so that
 (3)

where the s are Fibonacci Numbers.

The Fibonacci polynomials are related to the Morgan-Voyce Polynomials by

 (4) (5)

(Swamy 1968).

References

Swamy, M. N. S. Further Properties of Morgan-Voyce Polynomials.'' Fib. Quart. 6, 167-175, 1968.