Richard A. Askey

Certain functions occur so often that they are named "special functions." My research interest centers on two important classes of special functions: hypergeometric and basic hypergeometric series. Among the results found are the evaluation of some integrals that extend the gamma and beta integrals of Euler. Some of these are weight functions of new sets of orthogonal polynomials. Earlier, some inequalities were found that later played a role in de Branges's solution of the Bieberbach conjecture. This was a pleasant surprise, as was the setting of quantum groups that others found for some of the new orthogonal polynomials. Much of my work on basic hypergeometric series had utilized the results of S. Ramanujan as background information.