Some recurrence relations and their parallel evaluation using nested recurrent product form algorithm

Recurrence relations for the Fourier expansion of the Jacobian elliptic functions snm(u, k), cnm(u, k), dnm(u, k) with m⩾1 and those for the expansion of sinm(πx), cosm(πx) in powers of the Jacobian elliptic functions with m⩾1 are studied and their parallel evaluation is formulated using nested recurrent product form algorithm.Recurrence relations for the Fourier expansion of the Jacobian elliptic functions snm(u, k), cnm(u, k), dnm(u, k) with m⩾1 and those for the expansion of sinm(πx), cosm(πx) in powers of the Jacobian elliptic functions with m⩾1 are studied and their parallel evaluation is formulated using nested recurrent product form algorith