On the convergence of Padé-type approximants to analytic functions

摘要

For a given summability method, the Okada theorem describes a domain, into which an arbitrary power series can be analytically continued, if such a domain is known for the geometric series. In this paper, Okada's theorem is extended to more general methods of analytic continuation. This results is applied to a special rational approximation, the so-called Padé-type approximation.