Heisenberg algebra, umbral calculus and orthogonal polynomials

DOI10.1063/1.2909731zbMath1152.81396arXiv0712.2957OpenAlexW2008632008MaRDI QIDQ5504920

Decio Levi, Pavel Winternitz, Giuseppe Dattoli

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/0712.2957

Mathematics Subject Classification ID

Umbral calculus (05A40) 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) Quantum optics (81V80) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (11)

Degenerate poly-Cauchy polynomials with a \(q\) parameter ⋮ On poly-Bernoulli polynomials of the second kind with umbral calculus viewpoint ⋮ Barnes-type degenerate Euler polynomials ⋮ Direct spreading measures of Laguerre polynomials ⋮ Transmutations from the covariant transform on the Heisenberg group and an extended umbral principle ⋮ Degenerate poly-Cauchy polynomials ⋮ Degenerate Mittag-Leffler polynomials ⋮ Operational, umbral methods, Borel transform and negative derivative operator techniques ⋮ (Discrete) Almansi type decompositions: an umbral calculus framework based on osp(1|2) symmetries ⋮ Integrals of special functions and umbral methods ⋮ Barnes-type Peters polynomial with umbral calculus viewpoint

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