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Accessible Unlicensed Requires Authentication Published by De Gruyter February 28, 2017

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

Roman Wituła, Edyta Hetmaniok, Damian Słota and Mariusz Pleszczyński
From the journal Mathematica Slovaca

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.

MSC 2010: Primary 11B39; 11B83

(Communicated by Stanislav Jakubec)


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Received: 2013-3-27
Accepted: 2015-5-14
Published Online: 2017-2-28
Published in Print: 2017-2-1

© 2017 Mathematical Institute Slovak Academy of Sciences