Meixner–Pollaczek polynomials and the Heisenberg algebra

DOI10.1063/1.528394zbMath0672.33011OpenAlexW1969011660MaRDI QIDQ3825336

Koornwinder, Tom H.

Publication date: 1989

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528394

zbMATH Keywords

Heisenberg algebraMeixner-Pollaczek polynomialsHahn polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (23)

Integrable systems on the lattice and orthogonal polynomials of discrete variable ⋮ Vector orthogonal polynomials with Bochner's property ⋮ Orthogonal polynomials on the unit circle associated with the Laguerre polynomials ⋮ Generalized Meixner-Pollaczek polynomials ⋮ The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator ⋮ On the connection between continuous Hahn polynomials and the Heisenberg algebra ⋮ The Meixner--Pollaczek polynomials and a system of orthogonal polynomials in a strip ⋮ Quasinormal modes from Penrose limits ⋮ On Jacobi and continuous Hahn polynomials ⋮ A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials ⋮ Linearly-invariant families and generalized Meixner-Pollaczek polynomials ⋮ Operator orderings and Meixner-Pollaczek polynomials ⋮ Generalized Zernike or disc polynomials: an application in quantum optics ⋮ Toeplitz localization operators: spectral functions density ⋮ From sequences to polynomials and back, via operator orderings ⋮ Biorthogonal exponential sequences with weight function $\exp(ax^2+ibx)$ on the real line and an orthogonal sequence of trigonometric functions ⋮ The symmetric Meixner-Pollaczek polynomials with real parameter ⋮ Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials ⋮ Hausdorff moments, Hardy spaces, and power series ⋮ Orthogonal polynomials and operator orderings ⋮ Krylov complexity and orthogonal polynomials ⋮ Solution of the Hausdorff moment problem by the use of Pollaczek polynomials ⋮ Premixed-flame shapes and polynomials

Cites Work

• The Hahn and Meixner polynomials of an imaginary argument and some of their applications
• Continuous Hahn polynomials
• Continuous Hahn polynomials and the Heisenberg algebra
• The unitary irreducible representations of SL(2, R) in all subgroup reductions
• Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion

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