Stephen C MilneAffiliation: Ohio State University Email: milne.1@osu.edu Title Of Talk: A nonterminating $q$Dougall summation theorem for hypergeometric series in $U(n)$. Abstract: In this talk we extend important classical onevariable summations and transformations of Bailey to multiple basic hypergeometric series verywellpoised on unitary groups $U(n+1)$. In particular, we derive multivariable generalizations of Bailey's 3term transformation formula for ${}_8\phi_{7}$ series, and Bailey's nonterminating $q$Dougall summation formula. As pointed out by Michael Schlosser, our nonterminating $U(n+1)$ $q$Dougall summation formula yields a natural multivariable extension of Jacobi's classical identity for eighth powers of theta functions. All of this work is a consequence of the nonterminating $U(n+1)$ $q$Whipple transformation formula of Milne and Newcomb. This work is joint with Sheldon L. Degenhardt. WARNING: This page contains MATHJAX
Last update made Sun Feb 14 13:07:51 PST 2016.
