On (p, q) -classical orthogonal polynomials and their characterization theorems

Masjed Jamei, Mohammad; Soleyman, F; Area Carracedo, Iván Carlos; Nieto Roig, Juan José

doi:10.1186/s13662-017-1236-9

Masjed Jamei, Mohammad; Soleyman, F; Area Carracedo, Iván Carlos

; Nieto Roig, Juan José

DATE: 2017-06-29

UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/3245

EDITED VERSION: http://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-017-1236-9

UNESCO SUBJECT: 12 Matemáticas ; 1209 Estadística ; 1201.13 Polinomios

DOCUMENT TYPE: article

ABSTRACT

In this paper, we introduce a general (p,q)-Sturm-Liouville difference equation whose solutions are (p,q)-analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as (p,q)→(1,1). In this direction, some basic characterization theorems for the introduced (p,q)-Sturm-Liouville difference equation, such as Rodrigues representation for the solution of this equation, a general three-term recurrence relation, and a structure relation for the (p,q)-classical polynomial solutions are given.

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