Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin
We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u=−λx−2v+δ0 is also regular and symmetric Laguerre-Hahn linear form for every complex λ except for a discrete set of numbers depending on v. We explicitly give the coefficients of t...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/70835 |
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| author | M. Sghaier J. Alaya |
| author_facet | M. Sghaier J. Alaya |
| author_sort | M. Sghaier |
| collection | DOAJ |
| description | We show that if v
is a symmetric regular Laguerre-Hahn linear
form (functional), then the linear form u
defined by u=−λx−2v+δ0
is also regular and symmetric Laguerre-Hahn
linear form for every complex λ
except for a discrete set
of numbers depending on v. We explicitly give the coefficients
of the second-order recurrence relation, the structure relation of
the orthogonal sequence associated with u, and the class of the
linear form u knowing that of v. Finally, we apply the above
results to the symmetric associated form of the first order for
the classical polynomials. |
| format | Article |
| id | doaj-art-2eb75d156a6d45a3afaa1388b762e04b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2eb75d156a6d45a3afaa1388b762e04b2025-02-03T06:06:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/7083570835Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at originM. Sghaier0J. Alaya1Département de Mathématiques, Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Rue Omar Ibn El Khattab, 6072-Gabès, TunisiaFaculté des Sciences de Gabès, Université de Gabès, Route de Mednine, 6029-Gabès, TunisiaWe show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u=−λx−2v+δ0 is also regular and symmetric Laguerre-Hahn linear form for every complex λ except for a discrete set of numbers depending on v. We explicitly give the coefficients of the second-order recurrence relation, the structure relation of the orthogonal sequence associated with u, and the class of the linear form u knowing that of v. Finally, we apply the above results to the symmetric associated form of the first order for the classical polynomials.http://dx.doi.org/10.1155/IJMMS/2006/70835 |
| spellingShingle | M. Sghaier J. Alaya Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin International Journal of Mathematics and Mathematical Sciences |
| title | Building some symmetric Laguerre-Hahn functionals of
class two at most through
the sum of symmetric functionals as
pseudofunctions with a Dirac measure at origin |
| title_full | Building some symmetric Laguerre-Hahn functionals of
class two at most through
the sum of symmetric functionals as
pseudofunctions with a Dirac measure at origin |
| title_fullStr | Building some symmetric Laguerre-Hahn functionals of
class two at most through
the sum of symmetric functionals as
pseudofunctions with a Dirac measure at origin |
| title_full_unstemmed | Building some symmetric Laguerre-Hahn functionals of
class two at most through
the sum of symmetric functionals as
pseudofunctions with a Dirac measure at origin |
| title_short | Building some symmetric Laguerre-Hahn functionals of
class two at most through
the sum of symmetric functionals as
pseudofunctions with a Dirac measure at origin |
| title_sort | building some symmetric laguerre hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a dirac measure at origin |
| url | http://dx.doi.org/10.1155/IJMMS/2006/70835 |
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