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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 12, Pages 1909-1923

Extensions of Bailey's transform and applications

1106 Arihant Nagar, Kalka Mata Road, Udaipur, Rajasthan 313 001, India
2Department of Mathematics and Statistics, Maharana Bhupal College of Science, Mohanlal Sukhadia University, Udaipur, Rajasthan 313 001, India

Received 30 June 2004; Revised 9 May 2005

Copyright © 2005 Hindawi Publishing Corporation. 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.


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.