APPLICATIONS OF BASIC HYPERGEOMETRIC FUNCTIONS.

The application of basic hypergeometric functions to partitions is briefly discussed. It is shown how bilateral basic hypergeometric series have application in number theory (apart from partitions). The relationship between finite vector spaces and basic hypergeometric functions is discussed; the theory of Eulerian differential operators, which arose from the combinatorial theory of finite vector spaces, and which has interesting applications to basic hypergeometric series, is briefly described. Finally, the usefulness of both ordinary and basic hypergeometric functions in the proof of and classification of combinatorial identities, and some of the recent applications of basic hypergeometric functions in physics are discussed.