Convergence of the Rogers-Ramanujan continued fraction

Set q = exp(2piitau), where tau is an irrational number, and let R-q be the radius of holomorphy of the Rogers-Ramanujan function G(q)(z) = 1 + Sigma(n=1)(infinity) z(n) q(n2)/(1-q)...(1-q(n)). As is known, R-q less than or equal to 1 and for each alpha is an element of [0, 1] there exists q = q(alpha) such that R-q(alpha) = alpha. It is proved here that the function H-q(z) = G(q)(z)/G(q)(qz) is meromorphic not only in the disc = {\z\ < R-q}, but also in the disc D = {\z\ < 1}, which is larger for R-q < 1; and that the Rogers-Ramanujan continued fraction converges to H-q on compact subsets contained in D \ Omega(q), where Omega(q) is the union of circles with centres at z = 0 and passing through the poles of H-q. The convergence of the Rogers-Ramanujan continued fraction in the domain {\z\ < max (R-q, 1/2+\1+q\)}/Omega(q) was established earlier by Lubinsky.