## 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