Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #42 Dec 15 2024 04:36:41
%S 0,0,5,2,4,0,7,0,4,6,7,7,7,0,4,7,7,1,1,4,8,5,6,8,9,2,0,0,7,0,1,0,5,8,
%T 9,3,7,5,8,6,8,4,3,4,4,5,5,0,8,3,4,9,2,8,6,8,4,7,6,0,3,3,3,5,5,7,9,2,
%U 0,8,6,4,4,5,2,4,5,4,8,0,3,5,1,7,4,6,6,3,2,7,7,0,3,5,3,0,8
%N Decimal expansion of 4th du Bois-Reymond constant.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 237-239.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/duBois-ReymondConstants.html">du Bois-Reymond Constants</a>.
%F 2*Sum_{k>=1} (1 + (x_k)^2)^(-2) = (e^4 - 4*e^2 - 25)/8, where x_k is the k-th root of t = tan t and e = 2.71828... is the natural logarithm base.
%e 0.0052407046777047711...
%t RealDigits[(E^4 - 4E^2 - 25)/8, 10, 100][[1]]
%Y Cf. A138730 (continued fraction expansion).
%Y Cf. A062546 (c2), A224196 (c3), A243108 (c5), A245333 (c6).
%K nonn,cons
%O 0,3
%A _Alonso del Arte_, Feb 24 2012