A Convergence Based Study of Ramanujan’s h-functions Towards Enhancing Mathematical Understanding

The Ramanujan-Type Eisenstein series constitute a distinguished class of infinite series outlined by Ramanujan in his lost notebook. Through systematic derivation and analysis, this article demonstrates the relationships linking h-functions with Eisenstein series of varying levels. Further, we employ Ramanujan’s series to develop a range of differential identities associated with classical η-functions and h-functions. In addition, we present explicit identities that link Class One infinite series with h-functions through the incorporation of Eisenstein series of different levels.