A sequence of modular forms associated with higher-order derivatives of Weierstrass-type functions

Abstract

In this article, we first determine a sequence {fn(?)}n?N of modular forms with weight 2nk+4(2n-1-1) (n?N; k?N\{1}; N := {1,2,3,...}). We then present some applications of this sequence which are related to the Eisenstein series and the cusp forms. We also prove that higher-order derivatives of the Weierstrass type }2n-functions are related to the above-mentioned sequence {fn(?)}n?N of modular forms.