Fourier series of rational fractions of Jacobian elliptic functions (Q1177135)

The paper lists more than ninety Fourier series of rational fractions of Jacobian elliptic functions \[ f=f(u)=sn(u,k), \qquad =cn(u,k), \qquad =dn(u,k) \] (powers \(f^{\pm n}\), \(n=2,3,4\), and expressions with denominators \((1+af)^ m\), \(a\) constant, \(m=1,2\)), which are not found in known handbooks or in the list due to \textit{R. G. Langebartel} [SIAM J. Math. Anal. 11, 506-513 (1980; Zbl 0459.33001)]. Pointing out the method of evaluation of the Fourier coefficients - as usually with the help of the theory of residues -, the authors give an analytic method which is ''refreshingly concrete in this era of staggered abstraction'' and available for (e.g.) the study of chaotic motions in time-periodic perturbed integrable systems.