Dougall's Theorem

where  is a generalized hypergeometric function and  is the gamma function.

Bailey (1935, pp. 25-26) called the Dougall-Ramanujan identity "Dougall's theorem."

REFERENCES:

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 25-27, 1935.

Dougall, J. "On Vandermonde's Theorem and Some More General Expansions." Proc. Edinburgh Math. Soc. 25, 114-132, 1907.

Hardy, G. H. "A Chapter from Ramanujan's Note-Book." Proc. Cambridge Philos. Soc. 21, 492-503, 1923.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 84, 1998.

Whipple, F. J. W. "On Well-Poised Series, Generalized Hypergeometric Series Having Parameters in Pairs, Each Pair with the Same Sum." Proc. London Math. Soc. 24, 247-263, 1926.