Abstract and Applied Analysis

On the Complex Zeros of Some Families of Orthogonal Polynomials

Eugenia N. Petropoulou

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Abstract

The complex zeros of the orthogonal Laguerre polynomials L n ( a ) ( x ) for a < - n , ultraspherical polynomials P n ( λ ) ( x ) for λ < - n , Jacobi polynomials P n ( a , β ) ( x ) for a < - n , β < - n , a + β < - 2 ( n + 1 ) , orthonormal Al-Salam-Carlitz II polynomials P n ( a ) ( x ; q ) for a < 0 , 0 < q < 1 , and q -Laguerre polynomials L n ( a ) ( x ; q ) for a < - n , 0 < q < 1 are studied. Several inequalities regarding the real and imaginary properties of these zeros are given, which help locating their position. Moreover, a few limit relations regarding the asymptotic behavior of these zeros are proved. The method used is a functional analytic one. The obtained results complement and improve previously known results.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 263860, 14 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620737

Digital Object Identifier
doi:10.1155/2010/263860

Mathematical Reviews number (MathSciNet)
MR2660396

Zentralblatt MATH identifier
1200.30002

Citation

Petropoulou, Eugenia N. On the Complex Zeros of Some Families of Orthogonal Polynomials. Abstr. Appl. Anal. 2010 (2010), Article ID 263860, 14 pages. doi:10.1155/2010/263860. https://projecteuclid.org/euclid.aaa/1288620737


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