RELACIONES INVERSAS DE TIPO FINITO ENTRE SUCESIONES DE POLINOMIOS

Francisco Marcellán; Ridha Sfaxi

doi:10.18257/raccefyn.32(123).2008.2256

Vol. 32 No. 123 (2008), Mathematics

Vol. 32 No. 123 (2008)

INVERSE FINITE-TYPE RELATIONS BETWEEN SEQUENCES OF POLYNOMIALS

Mathematics

https://doi.org/10.18257/raccefyn.32(123).2008.2256

Published 2023-11-29

Francisco Marcellán⁺⁻
Ridha Sfaxi⁺⁻

Francisco Marcellán

Departamento de Matemáticas, Universidad Carlos lll de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain

Ridha Sfaxi

épartement des Méthodes Quantitatives, lnstitut Supérieur de Gestion de Gabes, Avenue Jilani Habib 6002, Gabes, Tunisie

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How to Cite

Marcellán, F., & Sfaxi, R. (2023). INVERSE FINITE-TYPE RELATIONS BETWEEN SEQUENCES OF POLYNOMIALS . Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 32(123), 245–255. https://doi.org/10.18257/raccefyn.32(123).2008.2256

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Abstract

Let φ be a monic polynomial, with deg φ = t ≥ 0. We say that there is a finite-type relation between two monic polynomial sequences {Bn}_n≥20 and {Qn}_n0 with respect to φ if there exists (s,r) Є N² , r ≥ s, such that.

where degΩ*_s (x;n)=s,n≥t. When the orthogonality of the two previous sequences is assumed, the inverse finite-type relation is always possible (11]. This work essentially studies
the case when only the sequence {Bn }n20 is orthogonal. In fact, we find necessary and sufficient conditions leading to inverse finite-type relations. In particular, the structure relation characterizing semi-classical sequences is a special case of the general situation. Sorne examples will be analyzed.

https://doi.org/10.18257/raccefyn.32(123).2008.2256

Keywords

Finite-type relations | recurrence relations | orthogonal polynomials | semiclassical polynomials

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References

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