Existence and Local Behavior of the Cubic Padé Approximation

This paper analyses the local behavior of the cubic function approximation of the form 3 ( ) ( ) ( ) ( ) ()P z f z Q z f z R z 2 (),p q rO z where (), (), ()P z Q z R z are algebraic polyno-mials of degree p,q,r respectively, to a function which has a given power series expansion about the origin. It is shown that the cubic Hermite-Padé form always defines a cubic function and that this function is analytic in a neighbourhood of the origin