Generating new classes of orthogonal polynomials
Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence Pn(x)+anPn−1(x)+bnPn−2(x), n≥1P0(x)=1,P−1(x)=0 to be orthogonal. In particular, we can find...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000919 |
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| _version_ | 1849686194188713984 |
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| author | Amílcar Branquinho Francisco Marcellán |
| author_facet | Amílcar Branquinho Francisco Marcellán |
| author_sort | Amílcar Branquinho |
| collection | DOAJ |
| description | Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect
to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters
an and bn
for the sequence
Pn(x)+anPn−1(x)+bnPn−2(x), n≥1P0(x)=1,P−1(x)=0
to be orthogonal. In particular, we can find explicitly the linear functional v such that the new
sequence is the corresponding family of orthogonal polynomials. Some applications for Hermite
and Tchebychev orthogonal polynomials of second kind are obtained. |
| format | Article |
| id | doaj-art-b6f42df6a10349d6b4cacced01eb2d76 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b6f42df6a10349d6b4cacced01eb2d762025-08-20T03:22:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119464365610.1155/S0161171296000919Generating new classes of orthogonal polynomialsAmílcar Branquinho0Francisco Marcellán1Departamento de Matemática, FCTUC, Universidade de Coimbra, Apartado 3008, Coimbra 3000, PortugalDepartamento de Ingeniería, Escuela Politécnica Superior, Universidad Carlos III, C. Butarque, 15, Leganés-Madrid 28911, SpainGiven a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence Pn(x)+anPn−1(x)+bnPn−2(x), n≥1P0(x)=1,P−1(x)=0 to be orthogonal. In particular, we can find explicitly the linear functional v such that the new sequence is the corresponding family of orthogonal polynomials. Some applications for Hermite and Tchebychev orthogonal polynomials of second kind are obtained.http://dx.doi.org/10.1155/S0161171296000919Orthogonal polynomialsLinear functionalsQuasi-orthogonality. |
| spellingShingle | Amílcar Branquinho Francisco Marcellán Generating new classes of orthogonal polynomials International Journal of Mathematics and Mathematical Sciences Orthogonal polynomials Linear functionals Quasi-orthogonality. |
| title | Generating new classes of orthogonal polynomials |
| title_full | Generating new classes of orthogonal polynomials |
| title_fullStr | Generating new classes of orthogonal polynomials |
| title_full_unstemmed | Generating new classes of orthogonal polynomials |
| title_short | Generating new classes of orthogonal polynomials |
| title_sort | generating new classes of orthogonal polynomials |
| topic | Orthogonal polynomials Linear functionals Quasi-orthogonality. |
| url | http://dx.doi.org/10.1155/S0161171296000919 |
| work_keys_str_mv | AT amilcarbranquinho generatingnewclassesoforthogonalpolynomials AT franciscomarcellan generatingnewclassesoforthogonalpolynomials |