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The Quarterly Journal of Mathematics Advance Access originally published online on October 20, 2007
The Quarterly Journal of Mathematics 2008 59(2):221-235; doi:10.1093/qmath/ham038
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

A MULTIPLE GENERALIZATION OF SLATER'S TRANSFORMATION FORMULA FOR A VERY-WELL-POISED-BALANCED 2r{psi}2r SERIES

Masahiko Ito{dagger}

Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 229-8558, Japan

{dagger} E-mail: mito{at}gem.aoyama.ac.jp

Received 28 November 2006; revised 20 June 2007
  Abstract

The Jackson integral of type BCn is a multiple generalization of a very-well-poised-balanced 2r{psi}2r basic hypergeometric series. Based on this fact, a multiple analogue of Slater's transformation formula for the 2r{psi}2r series is presented herein. The proposed formula also provides an extension of Gustafson's multiple 6{psi}6 summation formula of type Cn.


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