A PAGE ON EISENSTEIN SERIES IN RAMANUJANS LOST NOTEBOOK

Page 188 in Ramanujanʹs lost notebook is devoted to a certain class of infinite series connected with Eulerʹs pentagonal number theorem. These series are represented in terms of Ramanujanʹs famous Eisenstein series P, Q, and R. The purpose of this paper is to prove all the formulas on page 188 and to show that one of them leads to an interesting, new recurrence formula for (sigma) (n), the sum of the positive divisors of n.