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, differentialrecurrence
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.
