On Freud–Sobolev type orthogonal polynomials

Luis E. Garza*, Edmundo J. Huertas, Francisco Marcellán

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product 〈p,q〉1=∫Rp(x)q(x)e-x4dx+M0p(0)q(0)+M1p′(0)q′(0),where p, q are polynomials, M and M 1 are nonnegative real numbers. Connection formulas between these polynomials and Freud polynomials are deduced and, as an application, an algorithm to compute their zeros is presented. The location of their zeros as well as their asymptotic behavior is studied. Finally, an electrostatic interpretation of them in terms of a logarithmic interaction in the presence of an external field is given.

Original languageEnglish
Pages (from-to)505-528
Number of pages24
JournalAfrika Matematika
Issue number3-4
Publication statusPublished - 1 Jun 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

All Science Journal Classification (ASJC) codes

  • General Mathematics


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