Affiliation:
1. Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Abstract
Abstract
In this paper, with reference to the previous work [WITUŁA, R.—SŁOTA, 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.
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