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$\delta$-Fibonacci and $\delta$-Lucas numbers, $\delta$-Fibonacci and $\delta$-Lucas polynomials

In: Mathematica Slovaca, vol. 67, no. 1
Roman Wituła - Edyta Hetmaniok - Damian Słota - Mariusz Pleszczyński

Details:

Year, pages: 2017, 51 - 70
Keywords:
Fibonacci numbers, Lucas numbers, $\delta$-Fibonacci numbers
About article:
In this paper, with reference to the previous work [WITUŁA, R.---SŁOTA, D.: $\delta$-Fibonacci numbers, Appl. Anal. Discrete Math. 3 (2009), 310--329] concerning the, so called, $\delta$-Fibonacci numbers, the concepts of $\delta$-Lucas numbers, $\delta$-Fibonacci and $\delta$-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 $\delta$-Fibonacci numbers, also for $\delta$-Lucas numbers some attractive identities--bridges are obtained, connecting these numbers in practice with every sequence of integer numbers.
How to cite:
ISO 690:
Wituła, R., Hetmaniok, E., Słota, D., Pleszczyński, M. 2017. $\delta$-Fibonacci and $\delta$-Lucas numbers, $\delta$-Fibonacci and $\delta$-Lucas polynomials. In Mathematica Slovaca, vol. 67, no.1, pp. 51-70. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0247

APA:
Wituła, R., Hetmaniok, E., Słota, D., Pleszczyński, M. (2017). $\delta$-Fibonacci and $\delta$-Lucas numbers, $\delta$-Fibonacci and $\delta$-Lucas polynomials. Mathematica Slovaca, 67(1), 51-70. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0247
About edition:
Published: 1. 2. 2017