Gauss's Hypergeometric Theorem

for , where  is a (Gauss) hypergeometric function. If  is a negative integer , this becomes

which is known as the Chu-Vandermonde identity.

REFERENCES:

Bailey, W. N. "Gauss's Theorem." §1.3 in Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 2-3, 1935.

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 104, 1999.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 31, 1998.

Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, pp. 42 and 126, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.