A263031 Decimal expansion of a constant related to A262877 and A262947 (negated).

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

Offset

0,3

Links

Table of n, a(n) for n=0..105.

Formula

Integral_{x=0..infinity} 1/x*(exp(-x)/(1 - exp(-3*x))^2 - 1/(9*x^2) - 2/(9*x) - 5*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.

Example

-0.01453742918328403360502029450226209036054149759346444138152247405534...

Mathematica

NIntegrate[1/x*(Exp[-x]/(1 - Exp[-3*x])^2 - 1/(9*x^2) - 2/(9*x) - 5*Exp[-x]/36), {x, 0, Infinity}, WorkingPrecision -> 120, MaxRecursion -> 100, PrecisionGoal -> 110]

Crossrefs

Cf. A262876, A262877, A262946, A262947, A263030, A075700, A084448, A263405, A263414.

Sequence in context: A275275 A196402 A268741 * A004493 A348051 A328238

Adjacent sequences: A263028 A263029 A263030 * A263032 A263033 A263034

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 08 2015

Status

approved