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Meixner-Pollaczek polynomials and the Heisenberg algebra
Tom H. Koornwinder
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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
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Solution of the Hausdorff moment problem by the use of Pollaczek polynomials
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References
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Premixed-flame shapes and polynomials
Bruno Denet,Guy Joulin +1 more
TL;DR: In this paper, the nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames was studied, using pole-decompositions as starting point.
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On the connection between continuous Hahn polynomials and the Heisenberg algebra
Nora Brambilla,E. Montaldi +1 more
TL;DR: In this paper, an elementary proof for the connection between a system of continuous Hahn polynomials and symmetrizations of elements in the Heisenberg algebra is given.
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Linearly-invariant families and generalized Meixner–Pollaczek polynomials
TL;DR: In this article, the generalized Meixner-Pollaczek polynomials (GMP) were defined and studied, and a generalization of the Gegenbauer polynomial was proposed.
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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.