FILOMAT, vol.30, no.4, pp.1001-1004, 2016 (SCI-Expanded)
In this short paper, generally, we define a family of functions f(k) depends on the Eisenstein series with weight 2k, for k is an element of N. More detail, by considering the function fk, we define a derivative formula for generating weakly modular forms with weight 12. As a result for this, we claim that this formula gives an advantage to find the special solutions of some differential equations.