The proof of a formula concerning the asymptotic behavior of the reciprocal sum of the square of multiple-angle Fibonacci numbers

DOI10.1186/s13660-022-02755-7zbMath1506.11030OpenAlexW4210663989MaRDI QIDQ2129109

Pavel Trojovský, Diego Marques

Publication date: 22 April 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-022-02755-7

zbMATH Keywords

inequalitiesupper boundsFibonacciasymptoticseriesrecurrence sequences

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

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• On the reciprocal sums of the generalized Fibonacci sequences
• On the sum of reciprocal generalized Fibonacci numbers
• Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers
• More on the infinite sum of reciprocal Fibonacci, Pell and higher order recurrences
• A reciprocal sum related to the Riemann ζ-function
• On the Sum of Reciprocal Generalized Fibonacci Numbers
• On the reciprocal sums of products of Fibonacci and Lucas numbers
• On the sum of reciprocal of generalized bi-periodic Fibonacci numbers