2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59162The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum of two Γ-terms multiplied by terminating 3F2(1) series. A few such formulas were essentially known to Whipple in 1920's. Here we give a simpler and more complete overview of this type of evaluations. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to non-terminating series, and present a couple of similar generalizations of other known formulas.13 pages; classical proofs simplified, possible transformations reviewed; in the algoritmic part similar evaluations of other series addedClassical Analysis and ODEs33C05, 33F10, 39A10text