Euler matrices and their algebraic properties revisited
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 pol...
- Autores:
-
Quintana, Yamilet
Ramírez, William
Urieles
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/6443
- Acceso en línea:
- https://hdl.handle.net/11323/6443
http://dx.doi.org/10.18576/amis
https://repositorio.cuc.edu.co/
- Palabra clave:
- Euler polynomials
Euler matrix
Generalized Euler matrix
Generalized Pascal matrix
Fibonacci matrix
Lucas matrix
- Rights
- openAccess
- License
- CC0 1.0 Universal
| Summary: | 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. |
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