International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1909-1923
doi:10.1155/IJMMS.2005.1909
Extensions of Bailey's transform and applications
C.M. Joshi1
and Yashoverdhan Vyas2
1106 Arihant Nagar, Kalka Mata Road, Udaipur 313 001, Rajasthan, India
2Department of Mathematics and Statistics, Maharana Bhupal College of Science, Mohanlal Sukhadia University, Udaipur 313 001, Rajasthan, India
Abstract
The well-known Bailey's transform is extended. Using the extended transform, we derive hitherto undiscovered ordinary and q-hypergeometric identities and discuss their particular cases of importance, namely, two new q-sums for Saalschützian 4Φ3, new double series Rogers-Ramanujan-type identities of modulo 81, discrete extension of the q-analogs of two quadratic transformations of 2F1, and two new quadratic-cubic transformations of 3F2.