Volume no :44, Issue no: 1, March (2017)

Journal of Mathematical Sciences: Advances and Applications

THE INVERSE TAYLOR OPERATOR AND COMPLETELY MONOTONIC FUNCTIONS

Author's: Demetrios P. Kanoussis
Pages: [1] - [26]
Received Date: January 10, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121758

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 equation and examples involving the gamma and psi functions are given.

Keywords

difference operators, difference equations, complete monotonicity, gamma function, digamma (or psi) function.