The existence and local behaviour of the quadratic function approximation

AbstractThis paper analyses the local behaviour of the quadratic function approximation to a function which has a given power series expansion about the origin. It is shown that the quadratic Hermite-Padé form always defines a quadratic 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). If the discriminant has multiple zeros the order of the approximation will be degraded but only to a limited extent