\((p,q)\)-growth of meromorphic functions and the Newton-Padé approximant (Q2292318)

Summary: In this paper, we have considered the generalized growth (\((p,q)\)-order and \((p,q)\)-type) in terms of coefficient of the development \(p_{nn}\) given in the \((n,n)\)-th Newton-Padé approximant of meromorphic function. We use these results to study the relationship between the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of \(\mathbb{C}\) (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.