Engel Expansions and the Rogers–Ramanujan Identities Original Research Article

We study the previously developed extension of the Engel expansion to the field of Formal Laurent series. We examine three separate aspects. First we consider the algorithm in relation to the work of Ramanujan. Second we show how the algorithm can be used to prove expansions such as those found by Euler, Rogers, and Ramanujan. Finally we remark briefly on its use in acceleration of convergence.