Euler Matrices and their Algebraic Properties Revisited

Authors

Yamilet Quintana, Department of Pure and Applied Mathematics, Postal Code: 89000, Caracas 1080 A, Simon Bol ́ıvar University, VenezuelaFollow
William Ram ́ırez, Department of Natural and Exact Sciences, University of the Coast - CUC, Barranquilla, ColombiaFollow
Alejandro Urieles, Faculty of Basic Sciences - Mathematics Program, University of Atla ́ntico, Km 7, Port Colombia, Barranquilla, ColombiaFollow

Author Country (or Countries)

Venezuela

Abstract

This paper addresses the generalized Euler polynomial matrix E(α)(x) and the Euler matrix E. Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for E (α)(x) and define the inverse matrix of E . We establish some explicit expressions for the Euler polynomial matrix E (x), which involves the generalized Pascal, Fibonacci and Lucas matrices, respectively. From these formulae, we get some new interesting identities involving Fibonacci and Lucas numbers. Also, we provide some factorizations of the Euler polynomial matrix in terms of Stirling matrices, as well as a connection between the shifted Euler matrices and Vandermonde matrices.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140407

Recommended Citation

Quintana, Yamilet; Ram ́ırez, William; and Urieles, Alejandro (2020) "Euler Matrices and their Algebraic Properties Revisited," Applied Mathematics & Information Sciences: Vol. 14: Iss. 4, Article 7.
DOI: http://dx.doi.org/10.18576/amis/140407
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss4/7