# Stephen C Milne

Affiliation: 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 one-variable summations and transformations of Bailey to multiple basic hypergeometric series very-well-poised on unitary groups $U(n+1)$. In particular, we derive multivariable generalizations of Bailey's 3-term 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.