Irreducible representations of deformed oscillator algebra and q-special functions
Abstract
Different generators of a deformed oscillator algebra give rise to one-parameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the q-coherent states and with 'coordinate' operators - Jacobi matrices, are also pointed out.
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