AN APPROACH TO CONNECT THE RAMANUJAN-TYPE EISENSTEIN SERIES N(Q) WITH THETA FUNCTIONS FORMULATED BY BORWEIN

Ramanujan introduced novel categories of remarkable infinite series, referred to as the Ramanujan-type Eisenstein series, in his lost notebook. The present study utilizes the (p, k)-parametrization method developed by Alaca to examine the relationships between cubic theta functions of Borwein and Ramanujan-type Eisenstein series, especially N(q). By using Borwein’s theta functions, this method provides an innovative framework for determining Eisenstein series identities. Sum of an infinite series that converges to an infinite product is the primary focus of this study.