<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

Data publikacji: 21 wrz 2017

Zakres stron: 61 - 78

Otrzymano: 01 cze 2015

Przyjęty: 15 lip 2015

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

Słowa kluczowe
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

Data publikacji: 21 wrz 2017

Zakres stron: 61 - 78

Otrzymano: 01 cze 2015

Przyjęty: 15 lip 2015

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

Słowa kluczoweJacobsthal 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.

Słowa kluczowe
Jacobsthal polynomials, Lucas polynomials, generating function, generating matrix, Catalan's identity, d'Ocagne's identity