Srivastava, H.M.2009-08-242009-08-2419852009-08-24http://hdl.handle.net/1828/1572Simple proofs based only upon some rather elementary results are presented for several interesting generalizations (involving series with essentially arbitrary terms) a number of finite summation formulas for certain classes of hypergeometric functions of one and two variables. Applications of these general summation formulas to various multivariable hypergeometric functions, and their further generalizations (and unifications) and q-extensions, are also considered. The main results (2.3), (4.5), (6.1), (6.2) and (6.12) below, and their special cases including (for example) (2.1), (3.1), (3.5), (3.8), (4.1), (4.3), (5.1), (5.3) to (5.6), (6.14), (6.15) and (6.18), are believed to be new.entechnical reports (mathematics and statistics)Technical ReportDepartment of MathematicsDepartment of Mathematics and Statistics