<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥). We provide their properties and a generalization of the usual identities. We also present, for each one of these generalized polynomials, their ordinary generating functions and matrices. In the last part of the paper, we present some special kind of tridiagonal matrices whose entries are elements of these generalized polynomials.</abstract>

In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥). We provide their properties and a generalization of the usual identities. We also present, for each one of these generalized polynomials, their ordinary generating functions and matrices. In the last part of the paper, we present some special kind of tridiagonal matrices whose entries are elements of these generalized polynomials.

On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On Generalized Jacobsthal and Jacobsthal-Lucas polynomials"}

In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's...

On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Publicado en línea: 21 sept 2017

Páginas: 61 - 78

Recibido: 01 jun 2015

Aceptado: 15 jul 2015

DOI: https://doi.org/10.1515/auom-2016-0048

Palabras clave
Jacobsthal polynomials, Lucas polynomials, generating function, generating matrix, Catalan's identity, d'Ocagne's identity

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Publicado en línea: 21 sept 2017

Páginas: 61 - 78

Recibido: 01 jun 2015

Aceptado: 15 jul 2015

DOI: https://doi.org/10.1515/auom-2016-0048

Palabras claveJacobsthal polynomials, Lucas polynomials, generating function, generating matrix, Catalan's identity, d'Ocagne's identity

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Palabras clave
Jacobsthal polynomials, Lucas polynomials, generating function, generating matrix, Catalan's identity, d'Ocagne's identity