Put x = 1/18 and x = 17/90 in the identity:
gamma(x)*gamma(x+1/3)*gamma(x+2/3) = 2*pi*3^(1/2-3x)*gamma(3x),
and multiply the results together.
Warut
[Also caught by Dick Askey] Gack! Macsyma's and Mathematica's Gamma simplifiers are supposed to try that, so there are bugs in both! --rwg
On Thu, Aug 6, 2009 at 6:22 PM, <rwg@sdf.lonestar.org> wrote:
can be brutal! Can someone or something do
gamma(1/18)*gamma(17/90)*gamma(7/18)*gamma(47/90)*gamma(13/18)*gamma(77/90)/(gamma(1/6)*gamma(17/30)) = 4*3^(4/15)*%pi^2
1 17 7 47 13 77 gamma(--) gamma(--) gamma(--) gamma(--) gamma(--) gamma(--) 18 90 18 90 18 90 4/15 2 ----------------------------------------------------------- = 4 3 pi 1 17 gamma(-) gamma(--) 6 30 ? --rwg
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