A263178 Decimal expansion of a constant related to A263141 (negated).

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

Offset

0,2

Links

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

Formula

Integral_{x=0..infinity} exp(-4*x)/(x*(1 - exp(-5*x))^2) - 1/(25*x^3) - 1/(25*x^2) + 19/(300*x*exp(x)) dx.

A263178 + A263179 + A263180 + A263181 = (log(Gamma(1/5)^3 / ((1+sqrt(5)) * Pi * Gamma(3/5) * 5^(29/12))) - 4*Zeta'(-1))/5 = -0.2745843324986204888923185745... . - Vaclav Kotesovec, Oct 12 2015

Example

-0.126995867138823252945270574731135805611834188578689467298972164319...

Mathematica

NIntegrate[E^(-4*x)/(1-E^(-5*x))^2/x - 1/(25*x^3) - 1/(25*x^2) + 19*E^(-x)/(300*x), {x, 0, Infinity}, WorkingPrecision -> 120, MaxRecursion -> 100, PrecisionGoal -> 110]

Crossrefs

Cf. A263141, A263177, A263179, A263180, A263181.

Sequence in context: A136701 A175030 A335027 * A198230 A263495 A282079

Adjacent sequences: A263175 A263176 A263177 * A263179 A263180 A263181

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 11 2015

Status

approved