login
Decimal expansion of Product_{k>=1} (1 - exp(-2*k*Pi/sqrt(3))).
0

%I #10 May 23 2022 08:51:12

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

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

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

%N Decimal expansion of Product_{k>=1} (1 - exp(-2*k*Pi/sqrt(3))).

%C Note that Prudnikov incorrectly give this product as 3^(1/4)*exp(-Pi*sqrt(3)/18), which differs from the correct result by 0.0000182...

%D A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 757, section 6.2.3, incorrect formula 4.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>, formula 52.

%e 0.972713586936242371513055024334538082849547588619101318683993472802594...

%p evalf(Product(1 - exp(-2*k*Pi/sqrt(3)), k = 1..infinity), 105);

%t RealDigits[QPochhammer[E^(-2*Pi/Sqrt[3])], 10, 105][[1]]

%o (PARI) prodinf(k=1, (1 - exp(-2*k*Pi/sqrt(3))))

%Y Cf. A292828.

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, May 23 2022