Ebook: 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.