The divergence problem for multipoint Padé approximants of meromorphic functions

Abstract:The convergence theorem of de Montessus de Ballore type is satisfactory also for multipoint Padé approximants with very general interpolation schemes. The corresponding divergence result is less satisfactory. Here, as partial result, it is shown that an interpolation scheme of Kakehashi [1] from 1956 implies the divergence behaviour which you expect