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Print ISSN: 2944-9162, E-ISSN: 2732-9941 An Open Access International Journal of Applied Science and Engineering
Volume 4, 2024
A Note on Bivariate bi-periodic Mersenne Polynomials
Authors: , , ,
Abstract: We introduce a new generalization $$m_{n}$$(x,y), which we will call Bivariate Bi-periodic Mersenne polynomials depending on whether n is even or odd. We investigated the bivariate and biperiodic forms of Mersenne polynomials, focusing on their unique structural properties, roots, and relationships among coefficients. Key contributions include deriving the generating function and Binet formula, examining the limit behavior of the polynomials, and identifying connections between positive and negative terms. Also, we give the limits of the consecutive terms of the polynomials and some important identities such as Catalan, Cassini and D’Ocagne’s identity. We also find the corresponding binomial addition formula.
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Keywords: Mersenne sequence, Mersenne polynomials, Generalized Mersenne sequence, Bi-periodic sequence, Bivariate Bi-periodic sequence
Pages: 158-167
DOI: 10.37394/232020.2024.4.16