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A248179 Decimal expansion of (2/27)*(9 + 2*sqrt(3)*Pi).

%I A248179 #27 May 04 2023 01:56:10
%S A248179 1,4,7,2,7,9,9,7,1,7,4,3,7,4,3,0,1,5,5,8,1,9,5,9,0,3,3,6,7,2,9,8,4,6,
%T A248179 9,9,2,1,2,6,2,5,1,6,6,5,8,1,8,9,9,5,8,1,1,3,6,4,3,9,3,3,0,4,6,1,6,9,
%U A248179 4,3,6,3,6,0,5,6,1,5,7,2,8,1,6,3,7,3
%N A248179 Decimal expansion of (2/27)*(9 + 2*sqrt(3)*Pi).
%D A248179 J.-M. Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.1.q', p. 247.
%H A248179 Clark Kimberling, <a href="/A248179/b248179.txt">Table of n, a(n) for n = 1..1000</a>
%H A248179 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A248179 Equals Sum_{h >= 0} 1/binomial(2*h+1, h).
%F A248179 From _Amiram Eldar_, Nov 16 2021: (Start)
%F A248179 Equals 1 + Integral_{x>=0} 1/(x^2 + x + 1)^2 dx.
%F A248179 Equals 1 + Integral_{x>=1} 1/(x^2 - x + 1)^2 dx.
%F A248179 Equals Integral_{x=0..1} 1/(x^2 - x + 1)^2 dx. (End)
%F A248179 From _Bernard Schott_, Mar 18 2022: (Start)
%F A248179 Equals 2 * Sum_{n >= 1} (n!)^2/(2*n)!.
%F A248179 Equals 2 * A073016.
%F A248179 Equals hypergeometric function 2F1([1, 2], [3/2], x) at x=1/4. (End)
%e A248179 1.472799717437430155819590336729846992126251665818995811364393304616943...
%t A248179 r = 2/27 (9 + 2 Sqrt[3] \[Pi]); u = RealDigits[N[r, 200]][[1]]
%o A248179 (PARI) 2*(9+sqrt(12)*Pi)/27 \\ _Charles R Greathouse IV_, Sep 28 2022
%Y A248179 Cf. A073016, A091682, A248180.
%K A248179 nonn,easy,cons
%O A248179 1,2
%A A248179 _Clark Kimberling_, Oct 03 2014