XVIII.—On the Functions which are represented by the Expansions of the Interpolation-Theory

Let ƒ(x) be a given function of a variable x . We shall suppose that ƒ(x) is a one-valued analytic function, so that its Taylor's expansion in any part of the plane of the complex variable x can be derived from its Taylor's expansion in any other part of the plane by the process of analytic continuation.