National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore ; National Chung Cheng University, Department of Mathematics, Min-hsiung, Chiayi 621, Taiwan, Republic of China
Abstract:
In this paper, we derive some new identities satisfied by the series using Ramanujan's identities for , and . Our work is motivated by an attempt to develop a theory of elliptic functions to the septic base.