Gauss's Hypergeometric Theorem

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for 👁 R[c-a-b]>0
, where 👁 _2F_1(a,b;c;x)
is a (Gauss) hypergeometric function. If 👁 a
is a negative integer 👁 -n
, this becomes

which is known as the Chu-Vandermonde identity.

See also

Chu-Vandermonde Identity, Dougall's Formula, Generalized Hypergeometric Function, Hypergeometric Function, Thomae's Theorem

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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.

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Gauss's Hypergeometric Theorem

Cite this as:

Weisstein, Eric W. "Gauss's Hypergeometric Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GausssHypergeometricTheorem.html

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