OFFSET
1,1
COMMENTS
Constants from generalized Pi integrals: the case of n=12.
LINKS
Takayuki Tatekawa, Table of n, a(n) for n = 1..10001
FORMULA
Equals 2*Integral_{x=0..1} dx/sqrt(1-x^12).
Equals Beta(1/12, 1/2) / 6. - Peter Luschny, Apr 14 2024
Equals (1 + sqrt(3)) * Gamma(1/4)^2 / (4 * 3^(3/4) * sqrt(Pi)). - Vaclav Kotesovec, Apr 15 2024
EXAMPLE
2.2221586039664144669155853439....
MAPLE
Beta(1/12, 1/2) / 6: evalf(%, 89); # Peter Luschny, Apr 14 2024
MATHEMATICA
RealDigits[Sqrt[Pi]/6*Gamma[1/12]/Gamma[7/12], 10, 5001][[1]]
RealDigits[(1 + Sqrt[3]) * Gamma[1/4]^2 / (4 * 3^(3/4) * Sqrt[Pi]), 10, 120][[1]] (* Vaclav Kotesovec, Apr 15 2024 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Takayuki Tatekawa, Apr 12 2024
STATUS
approved