Eisenstein series and elliptic functions on Γ0(10)

We generalize two identities involving Eisenstein series given in Chapter 19 of Ramanujanʼs second notebook. Four infinite families of Eisenstein series are obtained and their properties are investigated. The generating function of each infinite family is shown to be an elliptic function which has a simple infinite product expansion. Transformation properties of the Eisenstein series are investigated from first principles without using the transformation properties of Dedekindʼs eta-function.