Stephen Milne

Affiliation: Ohio State University

Email: milne@math.ohio-state.edu

Title Of Talk: Basic Hypergeometric Series in $U(n+1)$ (and $C_n$) and extensions of works of Jacobi and Ramanujan

Abstract: We first review the Fundamental Theorem for $U(n+1)$ series and it's direct application to extend the main one-dimensional summation and transformation formulas of classical basic hypergeometric series. We then discuss some of our deeper extensions of the work of Bailey. We conclude with our $C_n$ corresponding generalizations of Jacobi's sums of squares formulas and Ramanujan's transformations for Mock Theta Functions.

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