Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 898274, 11 pages
doi:10.1155/2010/898274
Research Article

Approximation of Analytic Functions by Kummer Functions

Soon-Mo Jung

Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, Republic of Korea

Received 3 February 2010; Revised 27 March 2010; Accepted 31 March 2010

Academic Editor: Alberto Cabada

Copyright © 2010 Soon-Mo Jung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We solve the inhomogeneous Kummer differential equation of the form xy′′+(β-x)y′-αy=∑m=0∞amxm and apply this result to the proof of a local Hyers-Ulam stability of the Kummer differential equation in a special class of analytic functions.