A263179 Decimal expansion of a constant related to A263142 (negated).

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

Offset

0,2

Links

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

Formula

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

-0.187803021063745858976409657887070138806758984043175296048481791984...

Mathematica

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

Crossrefs

Cf. A263142, A263178, A263180, A263181.

Sequence in context: A319462 A086911 A327854 * A180311 A289913 A103984

Adjacent sequences: A263176 A263177 A263178 * A263180 A263181 A263182

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 11 2015

Status

approved