Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal   Polynomials
  We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of quadratic relation is illustrated by comparing two ways of calculating recursive coefficients. Finally, we derive a q-deformed version of the Toda equations for both q-Laguerre/Hermite ensembles. 
Chuan-Tsung Chan, Hsiao-Fan Liu
nlin.SI hep-th math-ph math.MP math.QA