scholarly journals Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off an arc

2001 ◽  
Vol 26 (8) ◽  
pp. 449-455
Author(s):  
R. Khaldi ◽  
R. Benzine
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Region Exterior ◽  
Discrete Part

We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc.

scholarly journals Three-fold symmetric Hahn-classical multiple orthogonal polynomials

2019 ◽  
Vol 18 (02) ◽  
pp. 271-332 ◽  
Author(s):  
Ana F. Loureiro ◽  
Walter Van Assche
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Symmetric Polynomial ◽  
Recurrence Coefficients ◽  
Absolute Value ◽  
Polynomial Sequences ◽  
Full Characterization ◽  
Classical Polynomials ◽  
Multiple Orthogonal Polynomials

We characterize all the multiple orthogonal three-fold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called the Hahn property and it is an extension of the concept of classical polynomials to the context of multiple orthogonality. The emphasis is on the polynomials whose indices lie on the step line, also known as [Formula: see text]-orthogonal polynomials. We explain the relation of the asymptotic behavior of the recurrence coefficients to that of the largest zero (in absolute value) of the polynomial set. We provide a full characterization of the Hahn-classical orthogonality measures supported on a [Formula: see text]-star in the complex plane containing all the zeros of the polynomials. There are essentially three distinct families, one of them [Formula: see text]-orthogonal with respect to two confluent functions of the second kind. This paper complements earlier research of Douak and Maroni.

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