A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/40063 |
Resumo: | The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric function |
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7160 |
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A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysisClifford algebraHypercomplex analysisSturm-Liouville equationVietoris' numbersThe paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric functionWiley2024-01-11T10:51:33Z2021-08-09T00:00:00Z2021-08-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/40063eng0170-421410.1002/mma.7684Cação, IsabelFalcão, M. IreneMalonek, Helmuth R.Tomaz, Graçainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-05-06T04:51:00Zoai:ria.ua.pt:10773/40063Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-06T04:51Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
title |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
spellingShingle |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis Cação, Isabel Clifford algebra Hypercomplex analysis Sturm-Liouville equation Vietoris' numbers |
title_short |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
title_full |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
title_fullStr |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
title_full_unstemmed |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
title_sort |
A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
author |
Cação, Isabel |
author_facet |
Cação, Isabel Falcão, M. Irene Malonek, Helmuth R. Tomaz, Graça |
author_role |
author |
author2 |
Falcão, M. Irene Malonek, Helmuth R. Tomaz, Graça |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Cação, Isabel Falcão, M. Irene Malonek, Helmuth R. Tomaz, Graça |
dc.subject.por.fl_str_mv |
Clifford algebra Hypercomplex analysis Sturm-Liouville equation Vietoris' numbers |
topic |
Clifford algebra Hypercomplex analysis Sturm-Liouville equation Vietoris' numbers |
description |
The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric function |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-08-09T00:00:00Z 2021-08-09 2024-01-11T10:51:33Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/40063 |
url |
http://hdl.handle.net/10773/40063 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0170-4214 10.1002/mma.7684 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Wiley |
publisher.none.fl_str_mv |
Wiley |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
mluisa.alvim@gmail.com |
_version_ |
1817543884002033664 |