![_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) |
where 
is a generalized hypergeometric
function and 
is the gamma function (Bailey 1935, p. 16;
Koepf 1998, p. 32).
Watson's Theorem
See also
Generalized Hypergeometric Function, Watson-Whipple Transformation, Whipple's IdentityExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Watson's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WatsonsTheorem.html