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International Journal of Analysis
Volume 2013 (2013), Article ID 328032, 11 pages
http://dx.doi.org/10.1155/2013/328032
Research Article

General-Appell Polynomials within the Context of Monomiality Principle

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 22 September 2012; Accepted 6 December 2012

Academic Editor: Jacques Liandrat

Copyright © 2013 Subuhi Khan and Nusrat Raza. 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

A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases.