On series of polynomials orthogonal on the real axis (Q1924605)

In 1984 E. A. Rakhmanov introduced two classes of polynomials orthogonal on the whole real axis and on the nonnegative semiaxis, respectively, generalizing the classical Hermite and Laguerre polynomials. Based on Rakhmanov's results on the asymptotic properties of these orthogonal polynomials, we analyse the behaviour of the corresponding orthogonal series. We describe their regions of convergence and we derive new analogues to a theorem of overconvergence of Ostrowski's type, a Hadamard gap theorem and a result on the frequency of noncontinuable orthogonal series of Rakmanov's type similar to Fatou-Hurwitz-Pólya's famous theorem on power series.