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Decimal expansion of Pi/(12*sqrt(3)).
6

%I #17 Sep 28 2022 14:13:56

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

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

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

%N Decimal expansion of Pi/(12*sqrt(3)).

%D George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), Chapter 13 A Master Formula, p. 250.

%H Vincenzo Librandi, <a href="/A244977/b244977.txt">Table of n, a(n) for n = 0..10000</a>

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Integral_{x=0..1} (x^2*(1 + x^2))/(1 + x^2 + x^4)^2 dx.

%F Equals beta(3/2, 1/2)/(6*sqrt(3)), where 'beta' is Euler's beta function.

%F Equals Integral_{x>=0} 1/(x^2 + 3)^2 dx. - _Amiram Eldar_, Nov 16 2021

%e 0.15114994701951815421617318813684631102367218734106171463082374461567693176...

%t RealDigits[Pi/(12*Sqrt[3]), 10, 105] // First

%o (PARI) Pi/sqrt(432) \\ _Charles R Greathouse IV_, Sep 28 2022

%Y Cf. A244976.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Jul 09 2014