Multiple Gaussian Hypergeometric Series

A multiple Gaussian hypergeometric series is a hypergeometric series in two or more variables which reduces to the familiar Gaussian hypergeometric series, whenever only one variable is non-zero. Two interesting problems in the theory of multiple Gaussian hypergeometric series consist in constructing all distinct series and in establishing their regions of convergence. Both of these problems are rather straightforward for single series, and they have been completely solved in the case of double series. This book is the first to aim at presenting a systematic (and thorough) discussion of the complexity of these problems when the dimension exceeds two; indeed, it gives the complete solution of each of the problems in case of the triple Gaussian hypergeometric series.