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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| Main Authors: | , |
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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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |