Existence and local behavior of general cubic Hermite-Padé Approximation

This paper analyses the local behavior of the general cubic function approximation to a function which has a given power series expansion about the origin. It is shown that the general cubic Hermite-Padé form always defines a cubic function and that this function is analytic in a neighbourhood of the origin. This result holds even if the origin is a critical point of the function (i.e., the discriminant has a zero at the origin).