International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1909-1923
Extensions of Bailey's transform and applications
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2Department of Mathematics and Statistics, Maharana Bhupal College of Science, Mohanlal Sukhadia University, Udaipur 313 001, Rajasthan, India
Received 30 June 2004; Revised 9 May 2005
Copyright © 2005 C. M. Joshi and Yashoverdhan Vyas. 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
-hypergeometric identities and discuss their particular cases
of importance, namely, two new -sums for Saalschützian
, new double series Rogers-Ramanujan-type identities
of modulo 81, discrete extension of the -analogs of two
quadratic transformations of , and two new
quadratic-cubic transformations of .