FEW MORE RELATIONS PERTAINING DIFFERENTIAL IDENTITIES AND h-FUNCTIONS

Ramanujan’s lost notebook contains a wealth of mathematical discoveries, many of which broaden our understanding of modular forms, special functions, and infinite series. Among the notable concepts introduced are the Ramanujan-type Eisenstein series, a category of infinite series that exhibit extraordinary properties and often reveal deep connections to modular forms and number theory. This work builds on Ramanujan’s foundational contributions to unveil novel differential identities, creating a richer understanding of η-functions, h-functions, and their connections to modular forms and modern mathematics. By connecting the sum of the Ramanujan-type Eisenstein series to the Class one infinite series, we bridge the gap between the two representations. This creates a fundamental tool for mathematical analysis by enabling us to infer the convergence of one from the convergence of the other.