Intriguing Relationships among Eisenstein Series, Borewein’s Cubic Theta Functions, and the Class One Infinite Series

This article focuses on the application of the Ramanujan-type Eisenstein series to the formation of numerous differential identities. In this paper, utilizing Alaca’s (p,k) parametrization, we explore a few additional interesting links between Eisenstein Series and Borewein’s cubic theta functions. Further, we build a set of higher-order nonlinear differential equations that include Ramanujan’s function k(q). In addition, we formulate identities relating the Class one infinite series and Ramanujan’s k-function, using the relationship derived between Eisenstein and the Class one infinite series.