On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight

Abey S. Kelil, Alta S. Jooste and Appanah R. Appadu
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Abey S. Kelil: Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6019, South Africa
Alta S. Jooste: Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa
Appanah R. Appadu: Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6019, South Africa

Mathematics, 2021, vol. 9, issue 9, 1-28

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.

Keywords: orthogonal polynomials; Meixner; perturbed Meixner–Pollaczek; moments; recurrence coefficients; difference equations; differential equations; zeros (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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