A weighted extension of Fibonacci numbers
Combinatorics
2023-01-20 v1 Classical Analysis and ODEs
Number Theory
Abstract
We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the -Fibonacci polynomials appearing in Schur's work. The proofs of most of the identities are combinatorial, extending the proofs given by Benjamin and Quinn, and in the case, by Garrett. Some identities are proved by telescoping.
Keywords
Cite
@article{arxiv.2301.08016,
title = {A weighted extension of Fibonacci numbers},
author = {Gaurav Bhatnagar and Archna Kumari and Michael J. Schlosser},
journal= {arXiv preprint arXiv:2301.08016},
year = {2023}
}
Comments
14 pages, comments solicited