A244980 Decimal expansion of Pi/(2*sqrt(6)).

6, 4, 1, 2, 7, 4, 9, 1, 5, 0, 8, 0, 9, 3, 2, 0, 4, 7, 7, 7, 2, 0, 1, 8, 1, 7, 9, 8, 3, 5, 5, 0, 3, 2, 0, 5, 7, 3, 3, 6, 3, 0, 3, 3, 3, 7, 8, 2, 0, 4, 6, 1, 6, 1, 5, 5, 0, 6, 9, 4, 8, 0, 3, 3, 7, 8, 1, 9, 9, 4, 1, 1, 7, 5, 6, 5, 1, 1, 0, 5, 0, 5, 1, 6, 6, 4, 3, 4, 5, 9, 5, 2, 6, 1, 9, 7, 2, 2, 0, 3, 7, 2, 5, 7, 9, 7

Offset: 0

Author

Jean-François Alcover, Jul 09 2014

Keywords

• nonn
• cons
• easy

Examples

			0.6412749150809320477720181798355032057336303337820461615506948033781994...
		

References

• George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), Chapter 13 A Master Formula, p. 250.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Beta Function
• Index entries for transcendental numbers

Crossrefs

Cf. A244976, A244977, A244978, A244979.

Programs

Mathematica

RealDigits[Pi/(2*Sqrt[6]), 10, 106] // First

PARI

Pi/sqrt(24) \\ Charles R Greathouse IV, Oct 01 2022

Formula

Equals Integral_{x=0..1} (1 + x^2)/(1 + 4*x^2 + x^4) dx.

Equals beta(1/2, 1/2)/(2*sqrt(6)), where 'beta' is Euler's beta function.

From Amiram Eldar, Aug 15 2020: (Start)

Equals Integral_{x=0..oo} 1/(x^2 + 6) dx.

Equals Integral_{x=0..oo} 1/(2*x^2 + 3) dx.

Equals Integral_{x=0..oo} 1/(3*x^2 + 2) dx.

Equals Integral_{x=0..oo} 1/(6*x^2 + 1) dx. (End)

Equals Integral_{x = 0..1} 1/(2*x^2 + 3*(1 - x)^2) dx. - Peter Bala, Jul 22 2022