Form Sequences to Polynomials and Back, via Operator Orderings

Abstract

C.M. Bender and G. V. Dunne showed that linear combinations of words $q^k{p}^n{q}^{n-k}$, where $p$ and $q$ are subject to the relation $qp-pq=ı$, may be expressed as a polynomial in the symbol $z=\frac{1}{2}(qp+pq)$. Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

References in corpus (1)

• Orthogonal polynomials and operator orderings