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%I #18 Oct 01 2022 00:34:10
%S 5,1,4,0,4,1,8,9,5,8,9,0,0,7,0,7,6,1,3,9,7,6,2,9,7,3,9,5,7,6,8,8,2,8,
%T 7,1,6,3,0,9,2,1,8,4,4,1,2,7,1,2,4,5,1,1,7,9,2,3,6,1,9,4,6,6,7,8,1,2,
%U 7,3,3,4,5,0,1,0,0,0,2,7,3,0,7,3,0,0,9,0,3,1,4,4,3,6,7,4,5,9,5,4,0,7
%N Decimal expansion of 5 Pi^2/96.
%D Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See pp. 17-20.
%H Zafar Ahmed, <a href="http://www.jstor.org/stable/2695720">Problem 10884</a>, The American Mathematical Monthly, Vol. 108, No. 6 (2001), p. 566, <a href="http://www.jstor.org/stable/3072448">Definitely an Integral, solution to Problem 10884</a>, solved by Knut Dale, George L. Lamb, the proposer and others, ibid., Vol. 109, No. 7 (2002), pp. 670-671.
%H Zafar Ahmed, <a href="https://arxiv.org/abs/1411.5169">Ahmed's integral: the maiden solution</a>, arXiv:1411.5169 [math.HO], 2014.
%H Michael Penn, <a href="https://www.youtube.com/watch?v=Yv1HVY4wng8">Ahmed's Integral</a>, YouTube video, 2021.
%H Juan Pla, <a href="https://arxiv.org/abs/1505.03314">A tale of Two Integrals: The Probability and Ahmed's Integrals</a>, arXiv:1505.03314 [math.CA], 2015.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AhmedsIntegral.html">Ahmed's Integral</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F From _Amiram Eldar_, Aug 17 2020: (Start)
%F Equals Integral_{x=0..1} arctan(sqrt(x^2 + 2))/(sqrt(x^2 + 2) * (x^2 + 1)) dx (Ahmed, 2001; Borwein et al., 2004).
%F Equals (1/10) * Integral_{x=1..oo} log(x)/(x^5 + x) dx. (End)
%e 0.514041895...
%t RealDigits[5 Pi^2/96, 10 , 100][[1]] (* _Amiram Eldar_, Aug 17 2020 *)
%Y Cf. A019673, A098459, A102521, A244854.
%K nonn,cons,easy
%O 0,1
%A _Eric W. Weisstein_, Jun 30 2004
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