|
%I #37 Aug 21 2023 11:30:52
%S 1,2,2,4,7,4,4,8,7,1,3,9,1,5,8,9,0,4,9,0,9,8,6,4,2,0,3,7,3,5,2,9,4,5,
%T 6,9,5,9,8,2,9,7,3,7,4,0,3,2,8,3,3,5,0,6,4,2,1,6,3,4,6,2,8,3,6,2,5,4,
%U 8,0,1,8,8,7,2,8,6,5,7,5,1,3,2,6,9,9,2,9,7,1,6,5,5,2,3,2,0,1,1
%N Decimal expansion of sqrt(3/2).
%C Coordinate of a control point for a degree-5 integration formula for 7 points over the unit circle. [Stroud & Secrest]
%C Also real and imaginary part of sqrt(-3i). - _Alonso del Arte_, Dec 11 2012
%C Area of the quadrilateral obtained when slicing a unit cube with a plane passing through opposite vertices and the middle of opposite edges. See CNRS link. - _Michel Marcus_, Mar 26 2016
%H Daniel Starodubtsev, <a href="/A115754/b115754.txt">Table of n, a(n) for n = 1..10000</a>
%H Ana Rechtman, <a href="http://images.math.cnrs.fr/Mars-2016-3e-defi.html">Mars 2016, 3e défi</a>, Images des Mathématiques, CNRS, 2016.
%H A. H. Stroud, D. Secrest, <a href="http://dx.doi.org/10.1090/S0025-5718-1963-0161473-0">Approximate integration formulas for certain spherically symmetric regions</a>, Math. Comp. 17 (82) (1963) 105.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F Equals 2*A187110.
%F Equals Sum_{k>=0} binomial(1/2, k)/2^k. - _Bruno Berselli_, Sep 11 2015
%F From _Amiram Eldar_, Aug 02 2020: (Start)
%F Equals Product_{k>=0} (1 + (-1)^k/(6*k + 3)).
%F Equals Sum_{k>=0} binomial(2*k,k)/12^k.
%F Equals 1 + Sum_{k>=1} (2*k - 1)!!/((2*k)!! * 3^k). (End)
%F Equals A010464/2. - _R. J. Mathar_, Feb 23 2021
%e 1.2247448713915890490986420373529456959829737403283350642163...
%t RealDigits[Sqrt[3/2], 10, 105][[1]] (* _Alonso del Arte_, Dec 11 2012 *)
%Y Cf. A010464 (double), A187110 (half), A157697 (reciprocal).
%K nonn,easy,cons
%O 1,2
%A _Eric Desbiaux_, Jul 30 2008
|
