Abstract
This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an exponential deformation of the classical Meixner–Pollaczek measure. In this contribution, we investigate certain properties such as moments of finite order, some new recursive relations, concise formulations, differential-recurrence relations, integral representation and some properties of the zeros (quasi-orthogonality, monotonicity and convexity of the extreme zeros) of the corresponding perturbed polynomials. Some auxiliary results for Meixner–Pollaczek polynomials are revisited. Some applications such as Fisher’s information, Toda-type relations associated with these polynomials, Gauss–Meixner–Pollaczek quadrature as well as their role in quantum oscillators are also reproduced.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference43 articles.
1. Hypergeometric Orthogonal Polynomials and Their q-Analogues;Koekoek,2010
2. DLMF Handbook of Mathematical Functions,2010
3. Orthogonal Polynomials;Szego,1975
4. Linearization and connection problems for the symmetric Meixner-Pollaczek polynomials;Araaya;Int. J. Pure Appl. Math.,2004
5. The Meixner–Pollaczek polynomials and a system of orthogonal polynomials in a strip
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