Some applications of the Lagrange inversion formula for the k-Fibonacci numbers

2023/07/27 by Farhi, Bakir
#11B37 #11B65 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11B39 #Secondary 11B83

paper · doi:10.48550/arxiv.2307.14763

Abstract

The aim of this paper consists of providing summation formulas for the k-Fibonacci numbers (k ∈ ℤ, k ≥ 2) and their asymptotic equivalents in terms of generalized binomial coefficients. Our main tools are the Lagrange inversion formula and one of its consequences due to Hermite.

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