The infinite sum of the cubes of reciprocal pell numbers

DOI10.1186/1687-1847-2013-184zbMath1390.11043OpenAlexW2170149860WikidataQ59301262 ScholiaQ59301262MaRDI QIDQ1648739

Zhefeng Xu, Ting-Ting Wang

Publication date: 27 June 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-184

zbMATH Keywords

identityPell numbersfloor function

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (6)

Some computational formulas related the Riemann zeta-function tails ⋮ On the reciprocal sums of the generalized Fibonacci sequences ⋮ On integer parts of the reciprocal remainders of some sums ⋮ On the sum of reciprocal generalized Fibonacci numbers ⋮ Partial reciprocal sums of the Mathieu series ⋮ Some identities related to Riemann zeta-function

Cites Work

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• The infinite sum of reciprocal Pell numbers
• Restricted partitions and \(q\)-Pell numbers
• On the computing of the generalized order-\(k\) Pell numbers in log time
• \(q\)-Pell sequences and two identities of V. A. Lebesgue
• 132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers
• The generalized order-\(k\) Fibonacci-Pell sequence by matrix methods
• Arithmetic properties of \(q\)-Fibonacci numbers and \(q\)-Pell numbers

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