Abstract and Applied Analysis
Volume 2012 (2012), Article ID 190726, 17 pages
http://dx.doi.org/10.1155/2012/190726
Research Article

Functions Induced by Iterated Deformed Laguerre Derivative: Analytical and Operational Approach

Sladjana D. Marinković,1 Miomir S. Stanković,2 and Predrag M. Rajković3

1Department of Mathematics, Faculty of Electronic Engineering, University of Niš, 18000 Niš, Serbia
2Department of Mathematics, Faculty of Occupational Safety, University of Niš, 18000 Niš, Serbia
3Department of Mathematics, Faculty of Mechanical Engineering, University of Niš, 18000 Niš, Serbia

Received 27 December 2011; Accepted 23 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Sladjana D. Marinković et al. 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

The one-parameter deformed exponential function was introduced as a frame that enchases a few known functions of this type. Such deformation requires the corresponding deformed operations (addition and subtraction) and deformed operators (derivative and antiderivative). In this paper, we will demonstrate this theory in researching of some functions defined by iterated deformed Laguerre operator. We study their properties, such as representation, orthogonality, generating function, differential and difference equation, and addition and summation formulas. Also, we consider these functions by the operational method.