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A263181
Decimal expansion of a constant related to A263144.
5
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
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
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Oct 11 2015
STATUS
approved