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K(p, q) = (d/dnp)G(p, q) = cos(r, np) / (2irrpq) of the Fredholm-Poincare integral equations. It will be shown that D(p, q) = [cos(wP, nq) + 3 cos(«j" r) cos(nq, r)]/(2irrpq)

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Summary. The existence of attractive cycles constitutes a serious impediment to the solution of nonlinear equations by iterative methods. This problem is illustrated in the case of the solution of the equation z tan z= c, for complex values of c, by Newton's method. Relevant results from the theory of the iteration of rational functions are cited and extended to the analysis of this case, in which a meromorphic function is iterated. Extensive numerical results, including many attractive cycles, are summarized.

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