The principal investigator will study the fundamental properties of hypergeometric series, especially basic (q-) and multibasic hypergeometric series. He will also work on the harmonic analysis of Racah, q-Racah and Askey-Wilson orthogonal polynomials. In particular, the principal investigator will study summation, transformation and expansion formulas, product formulas and integral representations for basic hypergeometric series. Previous work on convolution structures, multipliers, product formulas and generating functions for certain systems of orthogonal polynomials will be extended to other classes of polynomials. In addition, he will employ his methods involving sums and integrals of squares of real-valued functions to investigate the location of zeros of entire functions.
