Watson's Theorem

 _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)),

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

See also

Generalized Hypergeometric Function, Watson-Whipple Transformation, Whipple's Identity

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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 Web Resource.

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