 |
for ![R[c-a-b]>0](/images/equations/GausssHypergeometricTheorem/Inline1.svg)
,
where 
is a (Gauss) hypergeometric function.
If 
is a negative integer 
, this becomes
 |
which is known as the Chu-Vandermonde identity.
Gauss's Hypergeometric Theorem
See also
Chu-Vandermonde Identity, Dougall's Formula, Generalized Hypergeometric Function, Hypergeometric Function, Thomae's TheoremExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Gauss's Hypergeometric TheoremCite this as:
Weisstein, Eric W. "Gauss's Hypergeometric Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssHypergeometricTheorem.html