A263181 Decimal expansion of a constant related to A263144.

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

Offset

0,2

Links

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

Formula

Integral_{x=0..infinity} exp(-x)/(x*(1 - exp(-5*x))^2) - 1/(25*x^3) - 4/(25*x^2) - 71/(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

0.1863826906247526303913683646299184833844240863417644091469236860419...

Mathematica

NIntegrate[E^(-x)/(1-E^(-5*x))^2/x - 1/(25*x^3) - 4/(25*x^2) - 71*E^(-x)/(300*x), {x, 0, Infinity}, WorkingPrecision -> 120, MaxRecursion -> 100, PrecisionGoal -> 110]

Crossrefs

Cf. A263144, A263178, A263179, A263180.

Sequence in context: A084895 A154719 A356034 * A298978 A199151 A343275

Adjacent sequences: A263178 A263179 A263180 * A263182 A263183 A263184

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 11 2015

Status

approved