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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
Citations
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Hausdorff Moments, Hardy Spaces, and Power Series
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References
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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.
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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
H.T. Koelink,J. Van der Jeugt +1 more
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The Hahn and Meixner polynomials of an imaginary argument and some of their applications
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