Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

Abstract

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions and $ h $-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and $ h $-functions, thereby establishing links between class one infinite series and $ h $-functions.

Keywords

• eisenstein series
• dedekind $ \eta $-function
• class one infinite series
• differential equations