|
%I #28 Oct 01 2022 14:12:08
%S 7,8,7,4,8,0,4,9,7,2,8,6,1,2,0,9,8,7,2,1,4,5,3,2,2,9,9,7,2,3,3,6,0,2,
%T 2,7,1,1,5,5,8,4,2,6,9,1,3,9,9,3,6,6,9,2,9,1,2,8,6,5,3,8,6,5,2,0,3,4,
%U 5,5,3,2,6,6,0,0,8,2,7,8,0,8,8,7,9,7,3
%N Decimal expansion of sqrt(2*Pi^3).
%C This is the case n=4 of Product_{i=1..n-1} Gamma(i/n) = sqrt((2*Pi)^(n-1)/n).
%C Continued fraction expansion: 7, 1, 6, 1, 79, 4, 7, 1, 1, 1, 1, 1, 1, 4, 2, 3, 73, 1, 2, 1, 14, 3, 2, 1, 1, 2, 3, 1, ...
%H Vincenzo Librandi, <a href="/A220610/b220610.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#Products">Particular values of the Gamma function: Products</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals A002193*A175476.
%e 7.8748049728612098721453229972336022711558426913993669291...
%p evalf(sqrt(2*Pi^3),120); # _Muniru A Asiru_, Sep 30 2018
%t RealDigits[Sqrt[2 Pi^3], 10, 90][[1]]
%o (Maxima) fpprec:90; ev(bfloat(sqrt(2*%pi^3)));
%o (PARI) default(realprecision, 100); sqrt(2*Pi^3) \\ _G. C. Greubel_, Sep 29 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Pi(R)^3); // _G. C. Greubel_, Sep 29 2018
%Y Cf. numbers of the form sqrt((2*Pi)^(n-1)/n) -- see the first comment: A002161 (n=2), A186706 (n=3).
%K nonn,cons
%O 1,1
%A _Bruno Berselli_, Dec 25 2012
|
