- Research Article
- Open Access
© M.Wang and X. Zhao. 2009
- Received: 18 December 2008
- Accepted: 24 March 2009
- Published: 31 March 2009
- Real Number
- Ratio Test
- Nonnegative Integer
- Hypergeometric Series
- Compact Notation
is absolutely convergent. From (3.13), it is sufficient to establish that (3.2) is absolutely convergent.
Thereby, (3.16) diverges.
one knows that (4.3) converges absolutely.
one knows that (4.6) diverges.
The authors would like to express deep appreciation to the referees for the helpful suggestions. In particular, the authors thank the referees for help to improve the presentation of the paper. Mingjin Wang was supported by STF of Jiangsu Polytechnic University.
- Ito M: Convergence and asymptotic behavior of Jackson integrals associated with irreducible reduced root systems. Journal of Approximation Theory 2003,124(2):154–180. 10.1016/j.jat.2003.08.006MathSciNetView ArticleMATHGoogle Scholar
- Wang M: An inequality for and its applications. Journal of Mathematical Inequalities 2007,1(3):339–345.MathSciNetView ArticleMATHGoogle Scholar
- Wang M: Two inequalities for and applications. Journal of Inequalities and Applications 2008, 2008:-6.Google Scholar
- Andrews GE: The Theory of Partitions, Encyclopedia of Mathematics and Its Applications. Volume 2. Addison-Wesley, Reading, Mass, USA; 1976:xiv+255.Google Scholar
- Gasper G, Rahman M: Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications. Volume 35. Cambridge University Press, Cambridge, Mass, USA; 1990:xx+287.MATHGoogle Scholar
- Thomae J: Beiträge zur Theorie der durch die Heine'sche Reihe darstellbaren Funktionen. Journal für die reine und angewandte Mathematik 1869, 70: 258–281.MathSciNetView ArticleGoogle Scholar
- Thomae J: Les séries Heinéennes supérieures, ou les séries de la forme . Annali di Matematica Pura ed Applicata 1870, 4: 105–138.View ArticleGoogle Scholar
- Jackson FH: On -definite integrals. Quarterly Journal of Pure and Applied Mathematics 1910, 50: 101–112.Google Scholar
This article is published under license to BioMed Central Ltd. 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.