Orthogonal Polynomials with Singularly Perturbed Freud Weights

In this paper, we are concerned with polynomials that are orthogonal with respect to the singularly perturbed Freud weight functions. By using Chen and Ismail's ladder operator approach, we derive the difference equations and differential-difference equations satisfied by the recurrence coeffic...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2023-05, Vol.25 (5), p.829
Main Authors: Min, Chao, Wang, Liwei
Format: Article
Language:English
Subjects:
Coefficients
Difference equations
differential and difference equations
Differential equations
Mathematical analysis
Numerical analysis
Operators (mathematics)
orthogonal polynomials
Polynomials
Quantum field theory
recurrence coefficients
singularly perturbed Freud weights
Weighting functions
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Summary:In this paper, we are concerned with polynomials that are orthogonal with respect to the singularly perturbed Freud weight functions. By using Chen and Ismail's ladder operator approach, we derive the difference equations and differential-difference equations satisfied by the recurrence coefficients. We also obtain the differential-difference equations and the second-order differential equations for the orthogonal polynomials, with the coefficients all expressed in terms of the recurrence coefficients.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25050829