Domain of convergence for a series of orthogonal polynomials

Let {pk}k=0∞ be the orthogonal polynomials with certain exponential weights. In this paper, we prove that under certain mild conditions on exponential weights class, a series of the form ∑bkpk∑bkpk converges uniformly and absolutely on compact subsets of an open strip in the complex plane, and diverges at every point outside the closure of this strip.