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A244980 Decimal expansion of Pi/(2*sqrt(6)).

%I A244980 #20 Feb 16 2025 08:33:23
%S A244980 6,4,1,2,7,4,9,1,5,0,8,0,9,3,2,0,4,7,7,7,2,0,1,8,1,7,9,8,3,5,5,0,3,2,
%T A244980 0,5,7,3,3,6,3,0,3,3,3,7,8,2,0,4,6,1,6,1,5,5,0,6,9,4,8,0,3,3,7,8,1,9,
%U A244980 9,4,1,1,7,5,6,5,1,1,0,5,0,5,1,6,6,4,3,4,5,9,5,2,6,1,9,7,2,2,0,3,7,2,5,7,9,7
%N A244980 Decimal expansion of Pi/(2*sqrt(6)).
%D A244980 George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), Chapter 13 A Master Formula, p. 250.
%H A244980 Vincenzo Librandi, <a href="/A244980/b244980.txt">Table of n, a(n) for n = 0..10000</a>
%H A244980 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BetaFunction.html">Beta Function</a>
%H A244980 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A244980 Equals Integral_{x=0..1} (1 + x^2)/(1 + 4*x^2 + x^4) dx.
%F A244980 Equals beta(1/2, 1/2)/(2*sqrt(6)), where 'beta' is Euler's beta function.
%F A244980 From _Amiram Eldar_, Aug 15 2020: (Start)
%F A244980 Equals Integral_{x=0..oo} 1/(x^2 + 6) dx.
%F A244980 Equals Integral_{x=0..oo} 1/(2*x^2 + 3) dx.
%F A244980 Equals Integral_{x=0..oo} 1/(3*x^2 + 2) dx.
%F A244980 Equals Integral_{x=0..oo} 1/(6*x^2 + 1) dx. (End)
%F A244980 Equals Integral_{x = 0..1} 1/(2*x^2 + 3*(1 - x)^2) dx. - _Peter Bala_, Jul 22 2022
%e A244980 0.6412749150809320477720181798355032057336303337820461615506948033781994...
%t A244980 RealDigits[Pi/(2*Sqrt[6]), 10, 106] // First
%o A244980 (PARI) Pi/sqrt(24) \\ _Charles R Greathouse IV_, Oct 01 2022
%Y A244980 Cf. A244976, A244977, A244978, A244979.
%K A244980 nonn,cons,easy
%O A244980 0,1
%A A244980 _Jean-François Alcover_, Jul 09 2014