δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials

Abstract

In this paper, with reference to the previous work [WITULA, R. - SLOTA, D.: δ-Fibonacci numbers, Appl. Anal. Discrete Math. 3 (2009), 310-329] concerning the, so called, δ-Fibonacci numbers, the concepts of δ-Lucas numbers, δ-Fibonacci and δ-Lucas polynomials are introduced. There are discussed the basic properties of such objects, as well as their applications, especially for description of certain polynomials and identities of algebraic and trigonometric type. Many from among these identities describe the binomial transformations of the respective integer sequences and polynomials. Similarly as for δ-Fibonacci numbers, also for δ-Lucas numbers some attractive identities-bridges are obtained, connecting these numbers in practice with every sequence of integer numbers.