In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic fumctions sn(u,k), cn(u,k) and dn(u,k) are listed, which cannot be found in the handbood and Ref. [2]. For tile detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamihonian system subject to external periodic forcing by Melnikov’s method, and for studr of some problems of physical science and engineering, these formulas can be used.