Connection formulas for general discrete Sobolev polynomials: Mehler-Heine asymptotics

In this paper the discrete Sobolev inner product [p, q] = integral p(x)q(x)d mu+Sigma(r)(i=0)M(i)p((i))(c)q((i))(c) is considered, where mu is a finite positive Borel measure supported on an infinite subset of the real line, c is an element of R and M-i > 0, i = 0, 1, . . . . r. Connection formulas for the orthonormal polynomials associated with [., .] are obtained. As a consequence, for a wide class of measures mu, we give the Mehler-Heine asymptotics in the case of the point c is a hard edge of the support of mu. In particular, the case of a symmetric measure mu is analyzed. Finally, some examples are presented. (C) 2015 Elsevier Inc. All rights reserved.