Integration of Monomials over the Unit Sphere and Unit Ball in Rn
Descripción del Articulo
We compute the integral of monomials of the form x^2β over the unit sphere and the unit ball in R^n where β = (β1, . . . , βn) is a multi–index with real components βk > −1/2, 1 ≤ k ≤ n, and discuss their asymptotic behavior as some, or all, βk → ∞. This allows for...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de Publicación: | 2025 |
| Institución: | Universidad Nacional de Trujillo |
| Repositorio: | Revistas - Universidad Nacional de Trujillo |
| Lenguaje: | inglés |
| OAI Identifier: | oai:ojs.revistas.unitru.edu.pe:article/6616 |
| Enlace del recurso: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616 |
| Nivel de acceso: | acceso abierto |
| Materia: | Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n |
| id |
REVUNITRU_7c3e5a530fcbb33c6f111baab44cf65c |
|---|---|
| oai_identifier_str |
oai:ojs.revistas.unitru.edu.pe:article/6616 |
| network_acronym_str |
REVUNITRU |
| network_name_str |
Revistas - Universidad Nacional de Trujillo |
| repository_id_str |
|
| spelling |
Integration of Monomials over the Unit Sphere and Unit Ball in RnIntegration of Monomials over the Unit Sphere and Unit Ball in RnIntegration of Monomials over the Unit Sphere and Unit Ball in RnCalderón, Calixto P.Torchinsky, AlbertoIntegration over the Unit Sphere in R^nIntegration over the Unit Ball in R^nIntegration over the Unit Sphere in R^nIntegration over the Unit Ball in R^nIntegration over the Unit Sphere in R^nIntegration over the Unit Ball in R^nWe compute the integral of monomials of the form x^2β over the unit sphere and the unit ball in R^n where β = (β1, . . . , βn) is a multi–index with real components βk > −1/2, 1 ≤ k ≤ n, and discuss their asymptotic behavior as some, or all, βk → ∞. This allows for the evaluation of integrals involving circular and hyperbolic trigonometric functions over the unit sphere and the unit ball in Rn. We also consider the Fourier transform of monomials xα restricted to the unit sphere in Rn, where the multi–indices α have integer components, and discuss their behaviour at the origin.National University of Trujillo - Academic Department of Mathematics2025-07-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616Selecciones Matemáticas; Vol. 12 No. 01 (2025): January - July; 1 - 14Selecciones Matemáticas; Vol. 12 Núm. 01 (2025): Enero - Julio; 1 - 14Selecciones Matemáticas; v. 12 n. 01 (2025): Janeiro - Julho; 1 - 142411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUenghttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616/6852https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/66162025-07-26T15:43:48Z |
| dc.title.none.fl_str_mv |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn Integration of Monomials over the Unit Sphere and Unit Ball in Rn Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| title |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| spellingShingle |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn Calderón, Calixto P. Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n |
| title_short |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| title_full |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| title_fullStr |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| title_full_unstemmed |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| title_sort |
Integration of Monomials over the Unit Sphere and Unit Ball in Rn |
| dc.creator.none.fl_str_mv |
Calderón, Calixto P. Torchinsky, Alberto |
| author |
Calderón, Calixto P. |
| author_facet |
Calderón, Calixto P. Torchinsky, Alberto |
| author_role |
author |
| author2 |
Torchinsky, Alberto |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n |
| topic |
Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n Integration over the Unit Sphere in R^n Integration over the Unit Ball in R^n |
| description |
We compute the integral of monomials of the form x^2β over the unit sphere and the unit ball in R^n where β = (β1, . . . , βn) is a multi–index with real components βk > −1/2, 1 ≤ k ≤ n, and discuss their asymptotic behavior as some, or all, βk → ∞. This allows for the evaluation of integrals involving circular and hyperbolic trigonometric functions over the unit sphere and the unit ball in Rn. We also consider the Fourier transform of monomials xα restricted to the unit sphere in Rn, where the multi–indices α have integer components, and discuss their behaviour at the origin. |
| publishDate |
2025 |
| dc.date.none.fl_str_mv |
2025-07-26 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616 |
| url |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616/6852 |
| dc.rights.none.fl_str_mv |
https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| dc.source.none.fl_str_mv |
Selecciones Matemáticas; Vol. 12 No. 01 (2025): January - July; 1 - 14 Selecciones Matemáticas; Vol. 12 Núm. 01 (2025): Enero - Julio; 1 - 14 Selecciones Matemáticas; v. 12 n. 01 (2025): Janeiro - Julho; 1 - 14 2411-1783 reponame:Revistas - Universidad Nacional de Trujillo instname:Universidad Nacional de Trujillo instacron:UNITRU |
| instname_str |
Universidad Nacional de Trujillo |
| instacron_str |
UNITRU |
| institution |
UNITRU |
| reponame_str |
Revistas - Universidad Nacional de Trujillo |
| collection |
Revistas - Universidad Nacional de Trujillo |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1841449185092567040 |
| score |
13.439101 |
Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
