An infinite family of Engel expansions of Rogers-Ramanujan type

The extended Engel expansion is an algorithm that leads to unique series ex pansions of q-series. Various examples related to classical partition theor ems, including the: Rogers-Ramanujan identities, have been given recently. The object of this pa per is to show that the new and elegant Rogers-Ramanu jan generalization found by Garrett, Ismail, and Stanton also fits into thi s framework. This not only reveals the existence of an infinite, parameteri zed family of extended Engel expansions, but also provides an alternative p roof of the Garrett, Ismail, and Stanton result. A finite version of it, wh ich finds an elementary proof, is derived as a by-product of the Engel appr oach. (C) 2000 Academic Press.