Bi-periodic incomplete Lucas numbers
Nazmiye Yilmaz, Yasin Yazlik, Necati Taskara
TL;DR
This paper introduces bi-periodic incomplete Lucas numbers, deriving their recurrence relations, generating functions, and exploring their properties and relations to bi-periodic incomplete Fibonacci numbers.
Contribution
It presents the first formulation of bi-periodic incomplete Lucas numbers, including their recurrence, generating function, and connections to Fibonacci numbers.
Findings
Derived recurrence relation for bi-periodic incomplete Lucas numbers
Established generating function for these numbers
Explored relations between Lucas and Fibonacci variants
Abstract
In this paper, by presenting bi-periodic Lucas numbers as a binomial sum, we introduce the bi-periodic incomplete Lucas numbers. After that, by using the bi-periodic incomplete Lucas numbers, we derive the recurrence relation and the generating function of these numbers as well as investigated some properties over them. Additionally, as another main result of this paper, we give some relations between bi-periodic incomplete Lucas numbers and bi-periodic incomplete Fibonacci numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Biofield Effects and Biophysics