Kummer's first formula is

(1) 
where
is the Hypergeometric Function with , , , ..., and is the
Gamma Function. The identity can be written in the more symmetrical form as

(2) 
where and is a positive integer. If is a negative integer, the identity takes the form

(3) 
(Petkovsek et al. 1996).
Kummer's second formula is

(4) 
where
is the Confluent Hypergeometric Function and , , , ....
References
Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, pp. 4243 and 126, 1996.
© 19969 Eric W. Weisstein
19990526