Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
The Sobolev polynomials, which are orthogonal with respect to an inner product involving derivatives, are considered. The theory about these nonstandard polynomials has been developed along the last 40 years. The local asymptotics of these polynomials can be described by the Mehler-Heine formulae,...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2024
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/15252 |
| _version_ | 1789406427641544704 |
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| author | Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José |
| author_facet | Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José |
| author_sort | Mañas Mañas, Juan Francisco |
| collection | DSpace |
| description | The Sobolev polynomials, which are orthogonal with respect to an inner product involving derivatives, are considered. The theory
about these nonstandard polynomials has been developed along the last 40 years. The local asymptotics of these polynomials can be described by the Mehler-Heine formulae, which connect the polynomials with the Bessel functions of the first kind. In recent years, the formulae have been computed for discrete Sobolev orthogonal polynomials in several particular cases. We improve various known results by unifying them. Besides, an algorithm to compute these formulae effectively is presented. The algorithm allows to construct a computer program based on \ma \, language, where the corresponding Mehler-Heine formulae are automatically obtained. Applications and examples show the efficiency of the approach developed. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-15252 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2024 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-152522024-01-18T08:55:19Z Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José Sobolev orthogonal polynomials algorithm asymptotics computer program The Sobolev polynomials, which are orthogonal with respect to an inner product involving derivatives, are considered. The theory about these nonstandard polynomials has been developed along the last 40 years. The local asymptotics of these polynomials can be described by the Mehler-Heine formulae, which connect the polynomials with the Bessel functions of the first kind. In recent years, the formulae have been computed for discrete Sobolev orthogonal polynomials in several particular cases. We improve various known results by unifying them. Besides, an algorithm to compute these formulae effectively is presented. The algorithm allows to construct a computer program based on \ma \, language, where the corresponding Mehler-Heine formulae are automatically obtained. Applications and examples show the efficiency of the approach developed. 2024-01-18T08:55:18Z 2024-01-18T08:55:18Z 2022-04 info:eu-repo/semantics/article Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation East Asian J. Appl. Math. 12 (2022), 535--563. 2079-7370 http://hdl.handle.net/10835/15252 en Grant MTM2017-89941-P, grant grantUAL18- FQM-B025-A and grant SOMM17/6105/UGR. Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation East Asian J. Appl. Math. 12 (2022), 535--563. |
| spellingShingle | Sobolev orthogonal polynomials algorithm asymptotics computer program Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title | Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title_full | Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title_fullStr | Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title_full_unstemmed | Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title_short | Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation |
| title_sort | sobolev orthogonal polynomials: asymptotics and symbolic computation |
| topic | Sobolev orthogonal polynomials algorithm asymptotics computer program |
| url | http://hdl.handle.net/10835/15252 |
| work_keys_str_mv | AT manasmanasjuanfrancisco sobolevorthogonalpolynomialsasymptoticsandsymboliccomputation AT morenobalcazarjuanjose sobolevorthogonalpolynomialsasymptoticsandsymboliccomputation |