Expansion of analytic functions in exponential polynomials

Abstract

The expansion of analytic functions in interpolation series by the method of kernel expansion has been treated in [3], [4] and the detailed application of the method to expansions in the classical polynomials has culminated in the well-known monograph of Boas and Buck [2]. In the present paper we use the kernel expansion technique to obtain a new expansion in which the terms are not polynomials in the usual sense of powers but instead are the exponential polynomials