The Inverse Taylor Operator and Completely Monotonic Functions

Abstract

A new expansion of a function, inspired by the Taylor series expansion, is introduced, and various examples of functions admiting such new expansion, are given. In addition, it is shown that the new expansion, when applied to functions being completely monotonic, leads to some quite interesting results and applications. Finally, a new approach is suggested towards obtaining the solution of the difference equationand examples involving the gamma and psi functions are given.