A superintegrable discrete oscillator and two-variable Meixner polynomials
نویسندگان
چکیده
منابع مشابه
Laurent Polynomials and Superintegrable Maps
This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author’s recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Subsequently a family of fourth-order recurrences that share the Laurent property are considered, which a...
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Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable system a deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algeb...
متن کاملMeixner Polynomials and Random Partitions
The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov’s Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional...
متن کاملZeros of Meixner and Krawtchouk polynomials
We investigate the zeros of a family of hypergeometric polynomials 2F1(−n,−x; a; t), n ∈ N that are known as the Meixner polynomials for certain values of the parameters a and t. When a = −N, N ∈ N and t = p , the polynomials Kn(x; p,N) = (−N)n2F1(−n,−x;−N; p ), n = 0, 1, . . .N, 0 < p < 1 are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polyno...
متن کاملReal zeros of Meixner and Krawtchouk polynomials
We use a generalised Sturmian sequence argument and the discrete orthogonality of the Krawtchouk polynomials for certain parameter values to prove that all the zeros of Meixner polynomials are real and positive for parameter ranges where they are no longer orthogonal. AMS MOS Classification: 33C45, 34C10, 42C05
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2015
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/48/41/415202