OFFSET
0,1
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
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
EXAMPLE
0.6412749150809320477720181798355032057336303337820461615506948033781994...
MATHEMATICA
RealDigits[Pi/(2*Sqrt[6]), 10, 106] // First
PROG
(PARI) Pi/sqrt(24) \\ Charles R Greathouse IV, Oct 01 2022
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 09 2014
STATUS
approved