We argue that the Meixner polynomials of a discrete variable are actually “encoded” within appropriate infinite-dimensional irreducible unitary representations of the three-dimensional Lorentz group SO(2,1). Hence discrete series of irreducible unitary representation spaces of the non compact group SO(2,1) can be naturally interpreted as discrete versions of the linear harmonic oscillator in standard non-relativistic quantum mechanics.
"Meixner Polynomials and Representations of the 3D Lorentz Group SO(2,1)." Commun. Math. Anal. 17 (2) 14 - 23, 2014.