Results on sequences of Hermite-Padé, integral approximants

AbstractThe convergence of “horizontal” sequences of Hermite-Padé, integral approximants is studied by both numerical and theoretical methods. For functions with their nearest singularity of the algebraic type at z = 1 we complement previously proven convergence inside the unit circle by proving divergence outside the unit circle of sequences of the [L/M;1] type where M remains fixed and L → ∞