Almost holomorphic modular form

In mathematics, almost holomorphic modular forms are a generalization of modular forms that are polynomials in 1/Im(τ) with coefficients that are holomorphic functions of τ. A quasimodular form is the holomorphic part of an almost holomorphic modular form. The archetypal example of an almost homomorphic modular form is E₂(τ) – 3/πIm(τ), whose holomorphic part is the quasimodular Eisenstein series E₂(τ).