Hypergeometric series solutions of linear operator equations
Authors:
Qing-Hu Hou
Affiliation:
a Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China b College of Science, Tianjin University of Technology, Tianjin 300384, PR China
Abstract:
Let K be a field and L:K[x]→K[x] be a linear operator acting on the ring of polynomials in x over the field K. We provide a method to find a suitable basis {bk(x)} of K[x] and a hypergeometric term ck such that is a formal series solution to the equation L(y(x))=0. This method is applied to construct hypergeometric representations of orthogonal polynomials from the differential/difference equations or recurrence relations they satisfied. Both the ordinary cases and the q-cases are considered.