A263030 Decimal expansion of a constant related to A262876 and A262946 (negated).

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

Offset: 0

Author

Vaclav Kotesovec, Oct 08 2015

Keywords

• nonn
• cons

Examples

			-0.18870819197952853237641009864920797359211446726842922150941743378232...
		

Crossrefs

Cf. A262876, A262877, A262946, A262947, A263031, A075700, A084448, A263406, A263415.

Programs

Mathematica

NIntegrate[1/x*(Exp[-2*x]/(1 - Exp[-3*x])^2 - 1/(9*x^2) - 1/(9*x) + Exp[-x]/36), {x, 0, Infinity}, WorkingPrecision -> 120, MaxRecursion -> 100, PrecisionGoal -> 110]

Formula

Integral_{x=0..infinity} 1/x*(exp(-2*x)/(1 - exp(-3*x))^2 - 1/(9*x^2) - 1/(9*x) + exp(-x)/36) dx.

exp(3*(A263030+A263031)) = A^2 * Gamma(1/3) / (3^(11/12) * exp(1/6) * sqrt(2*Pi)), where A = A074962 is the Glaisher-Kinkelin constant.