Watson's theorem is the following generalized
hypergeometric function summation formula.
where 
is a generalized hypergeometric
function and 
is the gamma function (Bailey 1935, p. 16;
Koepf 1998, p. 32). The nonterminating series converges
for ![Re[2c-a-b]>-1](/images/equations/WatsonsTheorem/Inline3.svg)
.
See also
Generalized Hypergeometric Function,
Watson-Whipple Transformation,
Whipple's Identity
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References
Bailey, W. N. "Watson's Theorem." §3.3 in Generalised
Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 16,
1935.Koepf, W. Hypergeometric
Summation: An Algorithmic Approach to Summation and Special Function Identities.
Braunschweig, Germany: Vieweg, 1998.Referenced on Wolfram|Alpha
Watson's Theorem
Cite this as:
Weisstein, Eric W. "Watson's Theorem."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WatsonsTheorem.html
Subject classifications
![_3F_2[a,b,c; 1/2(a+b+1),2c;1]=(Gamma(1/2)Gamma(1/2+c)Gamma[1/2(1+a+b)]Gamma(1/2-1/2a-1/2b+c))/(Gamma[1/2(1+a)]Gamma[1/2(1+b)]Gamma(1/2-1/2a+c)Gamma(1/2-1/2b+c)),](/images/equations/WatsonsTheorem/NumberedEquation1.svg)
