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. 42-43 and 126, 1996.
© 1996-9 Eric W. Weisstein
1999-05-26