The uniform convergence of subsequences of the last intermediate row of the Padé table Original Research Article

In the work the uniform convergence of rows of the Padé approximants for a meromorphic function a(z) is studied. The complete description of the asymptotic behavior of denominators Qn(z) of the Padé approximants is obtained for the (λ−1)th row. Here λ is the number of the poles of a(z). The limits of all convergent subsequences of {Qn(z)} are explicitly computed. These limits form a family of polynomials which is parametrized by a monothetic subgroup F of the torus Tν. The group F is constructed via the arguments Θ1,…,Θν of those poles of a(z) of the maximal modulus that have the maximal multiplicity.