Theta functions and Eisenstein series

We define two elliptic functions and prove an identity connecting one function and a sum of Eisenstein series. We find a recurrence relation involving the Eisenstein series and Dedekind eta-products. We show equivalence of two elliptic functions under imaginary transformation and express the other function as an Eisenstein series. Combining the identity for the elliptic functions a curious identity related to a continued fraction found in Ramanujan's "lost" notebook is derived.