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%I #7 Dec 01 2018 08:59:32
%S 3,9,4,3,3,7,5,6,7,2,9,7,4,0,6,4,4,1,1,2,7,2,8,7,1,9,5,1,2,5,4,8,9,3,
%T 6,3,9,1,1,9,0,0,4,3,7,8,1,7,5,3,1,7,1,9,0,0,4,6,5,0,5,8,1,6,2,0,9,9,
%U 4,4,1,8,0,7,5,7,3,3,3,3,6,4,2,3,4,2,8
%N Decimal expansion of (3 + sqrt(3))/12.
%C The smallest weight in Holladay-Sard's quadrature formula for semi-infinite integrals.
%D Harold J. Ahlberg, Edwin N. Nilson and Joseph L. Walsh, The Theory of Splines and Their Applications, Academic Press, 1967.
%H John C. Holladay, <a href="https://doi.org/10.1090/S0025-5718-1957-0093894-6">A smoothest curve approximation</a>, Math. Comp. Vol. 11 (1957), 233-243.
%H Leroy F. Meyers and Arthur Sard, <a href="https://doi.org/10.1002/sapm1950291118">Best approximate integration formulas</a>, J. Math. Phys. Vol. 29 (1950), 118-123.
%H Arthur Sard, <a href="https://doi.org/10.2307/2372095">Best approximate integration formulas; best approximation formulas</a>, American Journal of Mathematics Vol. 71 (1949), 80-91.
%H Frans Schurer, <a href="https://research.tue.nl/en/publications/on-natural-cubic-splines-with-an-application-to-numerical-integra">On natural cubic splines, with an application to numerical integration formulae</a>, EUT report. WSK, Dept. of Mathematics and Computing Science Vol. 70-WSK-04 (1970), 1-32.
%F Equals lim_{n->infinity} A321118(0,n)/A321119(n).
%F Irrational number represented by the periodic continued fraction [0, 2, 1, 1; [6, 2]].
%F Largest real root of 1 - 12*x + 24*x^2.
%e 0.3943375672974064411272871951...
%p Digits := 1000; evalf((3 + sqrt(3))/12);
%t RealDigits[(3 + Sqrt[3])/12, 10, 100][[1]]
%o (PARI) (3 + sqrt(3))/12
%Y Cf. A020805, A165663.
%Y Cf. A321118, A321119.
%K nonn,easy,cons
%O 0,1
%A _Franck Maminirina Ramaharo_, Nov 09 2018
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