On Freud–Sobolev type orthogonal polynomials

Luis E. Garza; Edmundo J. Huertas; Francisco Marcellán

doi:10.1007/s13370-019-00663-6

On Freud–Sobolev type orthogonal polynomials

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	505-528
Number of pages	24
Journal	Afrika Matematika
Volume	30
Issue number	3-4
DOIs	https://doi.org/10.1007/s13370-019-00663-6
Publication status	Published - 1 Jun 2019
Externally published	Yes

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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title = "On Freud–Sobolev type orthogonal polynomials",

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.",

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doi = "10.1007/s13370-019-00663-6",

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T1 - On Freud–Sobolev type orthogonal polynomials

AU - Garza, Luis E.

AU - Huertas, Edmundo J.

AU - Marcellán, Francisco

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

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JO - Afrika Matematika

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ER -

On Freud–Sobolev type orthogonal polynomials

Abstract

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