Chebyshev series: Derivation and evaluation

In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial are also derived and summarized. Special case...

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Detalles Bibliográficos
Autores principales: Reynolds, Robert, Stauffer, Allan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9997935/
https://www.ncbi.nlm.nih.gov/pubmed/36893085
http://dx.doi.org/10.1371/journal.pone.0282703
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author Reynolds, Robert
Stauffer, Allan
author_facet Reynolds, Robert
Stauffer, Allan
author_sort Reynolds, Robert
collection PubMed
description In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial are also derived and summarized. Special cases are evaluated in terms of composite forms of both Chebyshev polynomials and the incomplete gamma function.
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spelling pubmed-99979352023-03-10 Chebyshev series: Derivation and evaluation Reynolds, Robert Stauffer, Allan PLoS One Research Article In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial are also derived and summarized. Special cases are evaluated in terms of composite forms of both Chebyshev polynomials and the incomplete gamma function. Public Library of Science 2023-03-09 /pmc/articles/PMC9997935/ /pubmed/36893085 http://dx.doi.org/10.1371/journal.pone.0282703 Text en © 2023 Reynolds, Stauffer https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Reynolds, Robert
Stauffer, Allan
Chebyshev series: Derivation and evaluation
title Chebyshev series: Derivation and evaluation
title_full Chebyshev series: Derivation and evaluation
title_fullStr Chebyshev series: Derivation and evaluation
title_full_unstemmed Chebyshev series: Derivation and evaluation
title_short Chebyshev series: Derivation and evaluation
title_sort chebyshev series: derivation and evaluation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9997935/
https://www.ncbi.nlm.nih.gov/pubmed/36893085
http://dx.doi.org/10.1371/journal.pone.0282703
work_keys_str_mv AT reynoldsrobert chebyshevseriesderivationandevaluation
AT staufferallan chebyshevseriesderivationandevaluation

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