Slater's Formula

Slater (1960, p. 31) terms the identity

for  a nonnegative integer the " summation theorem." Here,  is a generalized hypergeometric function with argument  and  is a Pochhammer symbol.

This is a special case of the more general identity

which holds for  (O. Marichev, pers. comm., May 16, 2008).

REFERENCES:

Slater, L. J. "An Elementary Proof of the  Summation Theorem." §2.7.1 in Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press, p. 31, 1960.