A class of finite q-series (Q760553)

In this first part of a series of three papers the author uses some simple ideas to prove an interesting unification (and generalization) of several finite summation formulas associated with various special hypergeometric functions of one and two variables. Further generalizations involving series with essentially arbitrary terms and their q-extensions are also presented. The main results and many of their special cases considered in this paper are believed to be new, and a number of known summation formulas are shown to follow easily by further particularizing some of these special cases.