ON THE MODIFIED CONVERGENCE OF SOME CONTINUED FRACTIONS OF ROGERS-RAMANUJAN TYPE

In this paper, the modified convergence of three Rogers-Ramanujan type continued fractions is established. These results are companions to well-known continued fraction identities of Rogers and Ramanujan and of Gordon. In the course of proving these modified convergence results, a simple and unified treatment of many partition identities of Rogers-Ramanujan type is proved using two q-series transformations. (C) 1994 Academic Press, Inc.