Abstract
In this paper we will use one well-known modular equation of seventh order, one theta function identity of S. McCullough and L.-C. Shen, 1994, and the complex variable theory of elliptic functions to prove some new septic identities for theta functions. Then we use these identities to provide new proofs of some Eisenstein series identities in Ramanujan's notebooks or lost notebook. We also derive a new identity for Eisenstein series and some curious trigonometric identities.
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