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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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References
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The Symmetric Meixner-Pollaczek polynomials
TL;DR: In this paper, the authors considered the problem of finding orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard's three term recurrence relation condition.
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Generalized Meixner-Pollaczek polynomials
Stanisława Kanas,Anna Tatarczak +1 more
TL;DR: In this paper, the generalized Meixner-Pollaczek polynomials P λ (x; θ, ψ )o f a variable x ∈ R and parameters λ > 0,θ ∈ (0, π ), ψ ∈ r,d ef ined via the generating function
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Global Asymptotics for Meixner‐Pollaczek Polynomials with a Varying Parameter
TL;DR: In this article, the uniform asymptotics of the Meixner-Pollaczek polynomials with varying parameter as, where A > 0 is a constant, were obtained.
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Representation theory and products of random matrices in $\text{SL}(2,{\mathbb R})$
TL;DR: In this paper, the authors studied the generalised Lyapunov exponent of a product of independent, identically distributed random matrices and derived explicit formulae for the almost-sure growth and variance of the corresponding products.
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Operator orderings and Meixner-Pollaczek polynomials
TL;DR: In this paper, the authors give identities which are generalizations of the formulas given by Koornwinder [J. Math. 30, (1989)] and Hamdi-Zeng [ J. Phys. 51, (2010)].