Irreducible representations of deformed oscillator algebra and q-special   functions
  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. 
E.V. Damaskinsky, P.P. Kulish