On the zeros of some d-orthogonal polynomials

被引：2
作者：
Ben Romdhane, Neila [1 ]
Abdelkader, Emna [1 ]
机构：
[1] Univ Sousse, Ecole Super Sci & Technol Hammam Sousse, Sousse, Tunisia
来源：
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2022年 / 33卷 / 10期
关键词：
d-orthogonal polynomials; recurrence relation; (d+1)-fold symmetric polynomials; Hessenberg matrix; d-Charlier polynomials; d-orthogonal Chebyshev polynomials; Gould-Hopper polynomials; GENERATING-FUNCTIONS;
D O I：
10.1080/10652469.2022.2043298
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give locations of the zeros of polynomials satisfying particular (d + 1)-order recurrence relations and we establish some representations of the smallest and largest real zeros of these polynomials in terms of the parameters in the (d + 1)-order recurrence relation. Particular interest is devoted to (d + 1) fold symmetric polynomials.
引用
收藏
页码：810 / 826
页数：17
相关论文
共 41 条
[1]   Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials [J].
Aptekarev, A. I. ;
Kalyagin, V. A. ;
Saff, E. B. .
CONSTRUCTIVE APPROXIMATION, 2009, 30 (02) :175-223
[2]   Multiple orthogonal polynomials [J].
Aptekarev, AI .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 99 (1-2) :423-447
[3]   Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials [J].
Aptekarev, AI ;
Marcellan, F ;
Rocha, IA .
JOURNAL OF APPROXIMATION THEORY, 1997, 90 (01) :117-146
[4]   Some discrete multiple orthogonal polynomials [J].
Arvesú, J ;
Coussement, J ;
Van Assehe, W .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 153 (1-2) :19-45
[5]   On the classical d-orthogonal polynomials defined by certain generating functions, I [J].
Ben Cheikh, Y ;
Douak, K .
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2000, 7 (01) :107-124
[6]   On the classical d-orthogonal polynomials defined by certain generating functions, II [J].
Ben Cheikh, Y ;
Douak, K .
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2001, 8 (04) :591-605
[7]   d-Symmetric d-orthogonal polynomials of Brenke type [J].
Ben Cheikh, Youssef ;
Ben Romdhane, Neila .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 416 (02) :735-747
[8]   On the zeros of d-symmetric d-orthogonal polynomials [J].
Ben Romdhane, N. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (02) :888-897
[9]   ON THE ZEROS OF d-ORTHOGONAL LAGUERRE POLYNOMIALS AND THEIR q-ANALOGUES [J].
Ben Romdhane, Neila .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (12) :5241-5249
[10]   GENERATING FUNCTIONS OF JACOBI AND RELATED POLYNOMIALS [J].
BRAFMAN, F .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 2 (06) :942-949
12345