%0 Journal Article
%T Hankel operators plus orthogonal polynomials yield combinatorial identities
%A E. A. Herman
%J Online Journal of Analytic Combinatorics
%D 2009
%I University of Auckland
%X A Hankel operator $H = [h_{i+j}]$ can be factored as $H = MM^ $, where $M$ maps a space of $L^2$ functions to the corresponding moment sequences. Furthermore, a necessary and sufficient condition for a sequence to be in the range of $M$ can be expressed in terms of an expansion in orthogonal polynomials. Combining these two results yields a wealth of combinatorial identities that incorporate both the matrix entries $h_{i+j}$ and the coefficients of the orthogonal polynomials.
%U http://analytic-combinatorics.org/index.php/ojac/article/view/57