From sequences to polynomials and back, via operator orderings
Résumé
Bender and Dunne ["Polynomials and operator orderings," J. Math. Phys. 29, 1727-1731 (1988)] showed that linear combinations of words q(k)p(n)q(n-k), where p and q are subject to the relation qp - pq = i, may be expressed as a polynomial in the symbol z = 1/2(qp + pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided