1303.6587 (T. Amdeberhan et al.)

Form Sequences to Polynomials and Back, via Operator Orderings    [PDF]

T. Amdeberhan, V. De Angelis, A. Dixit, V. H. Moll, C. Vignat

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 $qp - pq = \imath$, may be expressed as a polynomial in the symbol $z = \tfrac{1}{2}(qp+pq)$. Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

View original: http://arxiv.org/abs/1303.6587