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%I #25 Sep 28 2022 13:40:50
%S 2,7,7,6,8,0,1,8,3,6,3,4,8,9,7,8,9,0,4,3,8,4,9,2,5,6,1,8,7,8,7,9,3,3,
%T 5,6,1,6,3,4,1,3,8,5,5,5,8,5,9,8,0,6,3,8,9,4,2,8,3,7,2,2,5,4,3,4,7,7,
%U 7,1,7,4,5,6,8,7,1,7,1,1,9,4,1,0,9,5,7,9,3,3,4,2,2,7,9,7,8,2,7,3,3,5,2,1,3
%N Decimal expansion of Pi/(8*sqrt(2)).
%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="/A244976/b244976.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^4)^2 dx.
%F Equals beta(3/2, 1/2)/(4*sqrt(2)), where 'beta' is Euler's beta function.
%F Equals Sum_{k >= 0} (-1)^k * (2*k + 1)/((4*k + 1)*(4*k + 3)). - _Peter Bala_, Sep 21 2016
%F Equals Integral_{x>=0} 1/(x^2 + 2)^2 dx. - _Amiram Eldar_, Nov 16 2021
%e 0.277680183634897890438492561878793356163413855585980638942837225434777...
%t RealDigits[Pi/(8*Sqrt[2]), 10, 105] // First
%o (PARI) Pi/(8*sqrt(2)) \\ _G. C. Greubel_, Jul 05 2017
%Y Cf. A063448, A247719, A093954, A193887.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jul 09 2014