An Analysis of the Recurrence Coefficients for Symmetric Sobolev-Type Orthogonal Polynomials

Lino G. Garza, Luis E. Garza, Edmundo J. Huertas

Resultado de la investigaciónrevisión exhaustiva

Resumen

In this contribution we obtain some algebraic properties associated with the sequence of polynomials orthogonal with respect to the Sobolev-type inner product:〈p, q〉s =∫Rp(x)q(x)dµ(x) + M0 p(0)q(0) + M1 p′ (0)q′ (0), where p, q are polynomials, M0, M1 are non-negative real numbers and µ is a symmetric positive measure. These include a five-term recurrence relation, a three-term recurrence relation with rational coefficients, and an explicit expression for its norms. Moreover, we use these results to deduce asymptotic properties for the recurrence coefficients and a nonlinear difference equation that they satisfy, in the particular case when dµ(x) = e−x4 dx.
Idioma originalEnglish
Número de artículo534
PublicaciónSymmetry
Volumen13
N.º4
DOI
EstadoPublished - abr 2021

Nota bibliográfica

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© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

All Science Journal Classification (ASJC) codes

  • Informática (miscelánea)
  • Química (miscelánea)
  • Matemáticas (todo)
  • Física y astronomía (miscelánea)

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