Octabasic Laguerre polynomials and permutation statistics

A set of orthogonal polynomials with eight independent “qʹs” is defined which generalizes the Laguerre polynomials. The moments of the measure for these polynomials are the generating functions for permutations according to eight different statistics. Specializing these statistics gives many other well-known sets of combinatorial objects and relevant statistics. The specializations are studied, with applications to classical orthogonal polynomials and equidistribution theorems for statistics.