Open Access
Meixner-Pollaczek polynomials and the Heisenberg algebra
Tom H. Koornwinder
- pp 1-6
TLDR
In this paper, an alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. 28, 509 (1987)].Abstract:
An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.read more
Citations
More filters
Journal ArticleDOI
Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials
TL;DR: In this paper, the Meixner-Pollaczek polynomials were shown to recover pair of the known recurrence relations for the generalized Laguerre polynomial.
Journal ArticleDOI
A connection between operator orderings and representations of the Lie algebra \mathfrak{sl}_2
TL;DR: In this article, the authors investigate special classes of polynomials in the quantum mechanical position and momentum operators arising from various operator orderings, in particular from the so-called μ-orderings generalizing well-known operator ordering in quantum mechanics such as the Weyl ordering, the normal ordering, etc.
Some Properties Of Hypergeometric Meixner-Pollaczek Polynomials
Nejla Özmen,Hasan Göksu +1 more
TL;DR: In this paper, the Meixner-Pollaczek polynomials have been studied in many areas of mathematics and have been the subject of interest of many mathematicians.
References
More filters
Book
Groups and geometric analysis
TL;DR: Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata.
Posted Content
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
Journal ArticleDOI
Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
H.T. Koelink,J. Van der Jeugt +1 more
TL;DR: In this article, the authors derived convolution identities for Al-Salam and Chihara polynomials by using the Clebsch-Gordan decomposition and the Racah coefficients.
Journal ArticleDOI
The Hahn and Meixner polynomials of an imaginary argument and some of their applications
TL;DR: In this article, the Hahn and Meixner polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter, leading to the origination of two systems of real polynomial systems orthogonal with respect to a continuous measure.