<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.</p></abstract>

Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.

Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

Communications in Applied and Industrial Mathematics

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

{"article-title":"Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach"}

Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential...

Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

Online veröffentlicht: 05. Feb. 2019

Seitenbereich: 1 - 19

Eingereicht: 22. Nov. 2018

Akzeptiert: 22. Nov. 2018

DOI: https://doi.org/10.1515/caim-2019-0008

Schlüsselwörter
Translation operators, Hermite polynomials, Generating functions, Chebyshev polynomials, Gegenbauer polynomials

© 2019 Clemente Cesarano, published by Sciendo

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

Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

Online veröffentlicht: 05. Feb. 2019

Seitenbereich: 1 - 19

Eingereicht: 22. Nov. 2018

Akzeptiert: 22. Nov. 2018

DOI: https://doi.org/10.1515/caim-2019-0008

SchlüsselwörterTranslation operators, Hermite polynomials, Generating functions, Chebyshev polynomials, Gegenbauer polynomials

© 2019 Clemente Cesarano, published by Sciendo

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

Schlüsselwörter
Translation operators, Hermite polynomials, Generating functions, Chebyshev polynomials, Gegenbauer polynomials