A371929 Decimal expansion of Pi^(1/2)*Gamma(1/12)/(6*Gamma(7/12)).

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

Offset: 1

Author

Takayuki Tatekawa, Apr 12 2024

Keywords

• nonn
• cons

Comments

Constants from generalized Pi integrals: the case of n=12.

Examples

			2.2221586039664144669155853439....
		

Links

• Takayuki Tatekawa, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A085565, A113477, A262427, A371824.

Programs

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 *)

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