@skewray
Thanks for your article "Computing Generalized Hypergeometric Functions".

The thing that brought them to my attention was the marvelous book "A = B" by Marko Petkovsek, Herbert Wilf and Doron Zeilberger, foreword by Donald Knuth, 1996

""A=B" is about identities in general, and hypergeometric identities in particular..."

Now downloadable from its homepage:
https://www2.math.upenn.edu/~wilf/AeqB.html

P.S. My interest is not intended as a claim that I have mastered the area by any means. It is merely that, an interest.