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Decimal expansion of Product_{k=1..5} Gamma(k/3).
3

%I #10 Oct 12 2024 15:37:15

%S 2,9,2,4,3,2,7,2,2,9,9,5,2,4,0,2,5,5,3,7,2,8,7,3,8,0,7,4,0,3,7,3,7,8,

%T 1,1,4,1,6,7,0,2,2,0,4,6,5,8,9,8,6,3,8,8,9,3,0,7,6,5,9,0,7,4,4,3,5,5,

%U 6,8,8,3,6,2,7,2,3,5,7,1,0,9,0,3,7,5,6,2,4,8

%N Decimal expansion of Product_{k=1..5} Gamma(k/3).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GammaFunction.html">Gamma Function</a>.

%H <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>.

%F Equals Product_{k=1..6} Gamma(k/3) = (8/27)*Pi^2 = (8/27)*A002388 (cf. eqs. 87 and 88 in Weisstein link).

%F Equals 2*A214549. - _Hugo Pfoertner_, Oct 11 2024

%e 2.9243272299524025537287380740373781141670220...

%t First[RealDigits[8/27*Pi^2, 10, 100]]

%Y Cf. A002388, A214549.

%Y Other identities for Product_{k=1..m} Gamma(k/3): A073005 (m = 1), A186706 (m = 2 and m = 3), A376859 (m = 4), A376912 (m = 7), A376913 (m = 8).

%K nonn,cons

%O 1,1

%A _Paolo Xausa_, Oct 11 2024