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

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, 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, 4, 3, 6, 3, 6, 0, 5, 6, 1, 5, 7, 2, 8, 1, 6, 3, 7, 3

Offset: 1

Author

Clark Kimberling, Oct 03 2014

Keywords

• nonn
• easy
• cons

Examples

			1.472799717437430155819590336729846992126251665818995811364393304616943...
		

References

• J.-M. Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.1.q', p. 247.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for transcendental numbers

Crossrefs

Cf. A073016, A091682, A248180.

Programs

Mathematica

r = 2/27 (9 + 2 Sqrt[3] \[Pi]); u = RealDigits[N[r, 200]][[1]]

PARI

2*(9+sqrt(12)*Pi)/27 \\ Charles R Greathouse IV, Sep 28 2022

Formula

Equals Sum_{h >= 0} 1/binomial(2*h+1, h).

From Amiram Eldar, Nov 16 2021: (Start)

Equals 1 + Integral_{x>=0} 1/(x^2 + x + 1)^2 dx.

Equals 1 + Integral_{x>=1} 1/(x^2 - x + 1)^2 dx.

Equals Integral_{x=0..1} 1/(x^2 - x + 1)^2 dx. (End)

From Bernard Schott, Mar 18 2022: (Start)

Equals 2 * Sum_{n >= 1} (n!)^2/(2*n)!.

Equals 2 * A073016.

Equals hypergeometric function 2F1([1, 2], [3/2], x) at x=1/4. (End)