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 equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using s...
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doaj-4380efb717a44125a4ef651fc2374a3e2021-09-06T19:19:21ZengSciendoCommunications in Applied and Industrial Mathematics2038-09092019-01-0110111910.1515/caim-2019-0008caim-2019-0008Multi-Dimensional Chebyshev Polynomials: A Non-Conventional ApproachCesarano Clemente0Section of Mathematics, International Telematic University UNINETTUNO,Roma, ItalyChebyshev 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.https://doi.org/10.1515/caim-2019-0008translation operatorshermite polynomialsgenerating functionschebyshev polynomialsgegenbauer polynomials |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Cesarano Clemente |
spellingShingle |
Cesarano Clemente Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach Communications in Applied and Industrial Mathematics translation operators hermite polynomials generating functions chebyshev polynomials gegenbauer polynomials |
author_facet |
Cesarano Clemente |
author_sort |
Cesarano Clemente |
title |
Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach |
title_short |
Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach |
title_full |
Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach |
title_fullStr |
Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach |
title_full_unstemmed |
Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach |
title_sort |
multi-dimensional chebyshev polynomials: a non-conventional approach |
publisher |
Sciendo |
series |
Communications in Applied and Industrial Mathematics |
issn |
2038-0909 |
publishDate |
2019-01-01 |
description |
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. |
topic |
translation operators hermite polynomials generating functions chebyshev polynomials gegenbauer polynomials |
url |
https://doi.org/10.1515/caim-2019-0008 |
work_keys_str_mv |
AT cesaranoclemente multidimensionalchebyshevpolynomialsanonconventionalapproach |
_version_ |
1717778744875155456 |