ON THE VALUES OF CONTINUED FRACTIONS: q-SERIES II

Abstract

Let polynomials S(t), T(t) be given, then the convergence of the q-continued fraction [Formula: see text] will be studied using the Poincaré–Perron Theorem and Frobenius series solutions of the corresponding q-difference equation S(t)H(q2t) = -T(t)H(qt) + H(t). Our applications include a generalization of a q-continued fraction identity of Ramanujan and certain q-fractions, which arise in the theory of q-orthogonal polynomials.