On Freud–Sobolev type orthogonal polynomials
- Luis E. Garza,
- Edmundo J. Huertas,
- Francisco Marcellán
- Universidad de Colima,
- University of Alcalá,
- Universidad Carlos III de Madrid,
- Instituto de ciencias matemáticas (ICMAT)
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4
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0.96
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3
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70
Abstract
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.
Publication Information
Output type
Research Output:
Contribution to journal
Article
Peer-reviewOriginal language
EnglishPages from-to (Number of pages)
Pages 505-528 (24 pages)Journal (Volume, Issue Number)
Afrika Matematika (Volume 30, Issue 3-4)Publication milestones
- Published - 01/06/2019
Publication status
Published - 01/06/2019
ISSN
1012-9405Publication IDs
- Scopus: 85065904228
Funding Details
Acknowledgements We thank the anonymous referee for carefully reading the manuscript and for giving constructive comments, which substantially helped us to improve the quality of the paper. Part of this research was conducted while the first author was visiting the second author at the Universidad de Alcalá in early 2017, under the “GINER DE LOS RIOS” research program. Both authors wish to thank the Departamento de Física y Matemáticas de la Universidad de Alcalá for its support. The work of the three authors was partially supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, under Grant MTM2015-65888-C4-2-P. The work of the first author was also supported by Conacyt’s Grant 287523.
FundersFunding numbers
CONACYT
287523
MINECO
MTM2015-65888-C4-2-P
DGICT
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