Table of Contents
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 487546, 6 pages
http://dx.doi.org/10.1155/2013/487546
Research Article

-Analogues of Symbolic Operators

1College of Information and Mathematical Sciences, Clayton State University, Morrow, GA 30260-0285, USA
2Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA

Received 1 December 2012; Revised 15 May 2013; Accepted 21 June 2013

Academic Editor: Jun Ji

Copyright © 2013 Michael J. Dancs and Tian-Xiao He. 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

Here presented are -extensions of several linear operators including a novel -analogue of the derivative operator . Some -analogues of the symbolic substitution rules given by He et al., 2007, are obtained. As sample applications, we show how these -substitution rules may be used to construct symbolic summation and series transformation formulas, including -analogues of the classical Euler transformations for accelerating the convergence of alternating series.