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 q-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 q-case, by Garrett. Some identities are proved by telescoping.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have