(p; q)-Growth of Meromorphic Functions and the Newton-Pade Approximant

In this paper, we have considered the generalized growth ((p, q)-order and (p, q)-type) in term of
coefficient of the developpement pnn given by in the (n, n)-th Newton-pad´e approximant of meromorphic function.
We use these results to study the relationship betwen the degree of convergence in capacity of
interpolating functions and information on the degree of convergence of best rational approximation
on a compact of C (in the supremum norm). We will also show that the order of meromorphic
functions puts an upper bound on the degree of convergence.