Results on sequences of Hermite-Padé, integral approximants (Q686568)

The convergence of ``horizontal'' sequences of Hermite-Padé integral approximants has been studied by both numerical and analytic methods. ``Horizontal'' means here that the result is of Montessus de Ballore's type, all degree except the first one are kept fixed. For functions with their nearest singularity on an algebraic type at \(z=1\) a previous result has been complemented by proving divergence outside the unit circle for sequences of the \([L/M;1]\)-type where \(M\) remains fixed and \(L\to\infty\).