More on the q-oscillator algebra and q-orthogonal polynomials

Details More on the q-oscillator algebra and q-orthogonal polynomials More on the q-oscillator algebra and q-orthogonal polynomials

1995-04-26

arxiv.org/abs/math/9504218v1

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1088/0305-4470/28/10/002

Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this algebra. A realization is presented where the continuous $q$-Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big $q$-Hermite polynomials and the continuous $q$-Hermite polynomials is thus obtained, and two generating functions for these last polynomials are algebraically derived.

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