Abstract and Applied Analysis
Volume 2011 (2011), Article ID 923269, 13 pages
http://dx.doi.org/10.1155/2011/923269
Research Article

Approximation of Analytic Functions by Bessel's Functions of Fractional Order

Soon-Mo Jung

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

Received 31 March 2011; Accepted 6 June 2011

Academic Editor: Yong Zhou

Copyright © 2011 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 will solve the inhomogeneous Bessel's differential equation 𝑥 2 𝑦 ′ ′ ( 𝑥 ) + 𝑥 𝑦 ( 𝑥 ) + ( 𝑥 2 − 𝜈 2 ∑ ) 𝑦 ( 𝑥 ) = ∞ 𝑚 = 0 𝑎 𝑚 𝑥 𝑚 , where 𝜈 is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.