Table of Contents
Chinese Journal of Mathematics
Volume 2014 (2014), Article ID 716718, 5 pages
http://dx.doi.org/10.1155/2014/716718
Research Article

Translation, Creation and Annihilation of Poles and Zeros with the Biernacki and Ruscheweyh Operators, Acting on Meijer's -Functions

1Nuclear Science Research School, NSTRI, P.O. Box, Tehran 14395-836, Iran
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 17 November 2013; Accepted 2 January 2014; Published 12 February 2014

Academic Editors: S. Deng and N. Igbida

Copyright © 2014 Amir Pishkoo and Maslina Darus. 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

Meijer's G-functions are studied by the Biernacki and Ruscheweyh operators. These operators are special cases of the Erdélyi-Kober operators (for ). The effect of operators on Meijer's G-functions can be shown as the change in the distribution of poles and zeros on the complex plane. These poles and zeros belong to the integrand, a ratio of gamma functions, defining the Meijer's G-function. Displacement in position and increasing or decreasing in number of poles and zeroes are expressed by the transporter, creator, and annihilator operators. With special glance, three basic univalent Meijer's G-functions, Koebe, and convex functions are considered.