  The 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 \Gamma-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.
