On Leonardo Pisano Hybrinomials
Abstract
:1. Introduction
- (i)
- ⇔,
- (ii)
- ,
- (iii)
2. Leonardo Pisano Polynomials and Hybrinomials
3. Some Identities for Leonardo Pisano Polynomial and Hybrinomial Sequences
- i.
- ii.
- i.
- From the definition of Leonardo Pisano polynomial sequenceIn order to equalize the indexes, we add , , and to both sides. Therefore we can writeEventually, we obtain the desired result.
- ii.
- The proof can be demonstrated the same way.
- i.
- The Catalan-like identity for Leonardo Pisano polynomials is
- ii.
- The Catalan-like identity for Leonardo Pisano hybrinomials is
- i.
- The Cassini-like identity for Leonardo Pisano polynomials is
- ii.
- The Cassini-like identity for Leonardo Pisano hybrinomials is
- i.
- The d’Ocagne-like identity for Leonardo Pisano polynomials is
- ii.
- The d’Ocagne-like identity for Leonardo Pisano hybrinomials is
- i.
- Let us use the Binet-like formula for Leonardo Pisano polynomials.
- ii.
- This can be proven similarly to (i) using the Binet-like formula for Leonardo Pisano hybrinomials.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Kürüz, F.; Dağdeviren, A.; Catarino, P. On Leonardo Pisano Hybrinomials. Mathematics 2021, 9, 2923. https://doi.org/10.3390/math9222923
Kürüz F, Dağdeviren A, Catarino P. On Leonardo Pisano Hybrinomials. Mathematics. 2021; 9(22):2923. https://doi.org/10.3390/math9222923
Chicago/Turabian StyleKürüz, Ferhat, Ali Dağdeviren, and Paula Catarino. 2021. "On Leonardo Pisano Hybrinomials" Mathematics 9, no. 22: 2923. https://doi.org/10.3390/math9222923
APA StyleKürüz, F., Dağdeviren, A., & Catarino, P. (2021). On Leonardo Pisano Hybrinomials. Mathematics, 9(22), 2923. https://doi.org/10.3390/math9222923