Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Convergence of q-Series Involving r 1 φr Basic Hypergeometric Series | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 170526 9 pages doi 2009 170526 Research Article On Convergence of q-Series Involving r 1ộr Basic Hypergeometric Series Mingjin Wang1 and Xilai Zhao2 1 Department of Applied Mathematics Jiangsu Polytechnic University Changzhou Jiangsu 213164 China 2 Department of Mechanical and Electrical Engineering Hebi College of Vocation and Technology Hebi Henan 458030 China Correspondence should be addressed to Mingjin Wang wang197913@ Received 18 December 2008 Accepted 24 March 2009 Recommended by Ondrej Dosly We use inequality technique and the terminating case of the q-binomial formula to give some results on convergence of q-series involving r 1ịr basic hypergeometric series. As an application of the results we discuss the convergence for special Thomae q-integral. Copyright 2009 M. Wang and X. Zhao. 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. 1. Introduction q-Series which are also called basic hypergeometric series play a very important role in many fields such as affine root systems Lie algebras and groups number theory orthogonal polynomials and physics. Convergence of a q-series is an important problem in the study of q-series. There are some results about it in 1-3 . For example Ito used inequality technique to give a sufficient condition for convergence of a special q-series called Jackson integral. In this paper by using inequality technique we derive the following two theorems on convergence of q-series involving r 1ộr basic hypergeometric series which can be used for convergence of special Thomae q-integral. 2. Notations and Known Results We recall some definitions notations and known results which will be used in the proofs. Throughout this paper it is supposed that 0 q 1. The q-shifted .
