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Decimal expansion of a constant related to A263136 (negated).
3

%I #9 Jan 07 2021 07:29:14

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

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

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

%N Decimal expansion of a constant related to A263136 (negated).

%F Integral_{x=0..infinity} exp(-3*x)/(x*(1 - exp(-4*x))^2) - 1/(16*x^3) - 1/(16*x^2) + 5/(96*x*exp(x)) dx.

%F A263176 + A263177 = log(Gamma(1/4))/2 - Zeta'(-1)/4 - 2*log(2)/3 - log(Pi)/4 = -0.062914043561495455491893116973161914641792581828767341125... . - _Vaclav Kotesovec_, Oct 12 2015

%e -0.158924147180165035059952001737321408554746599955833696821824808027...

%t NIntegrate[E^(-3*x)/(1-E^(-4*x))^2/x - 1/(16*x^3) - 1/(16*x^2) + 5*E^(-x)/(96*x), {x, 0, Infinity}, WorkingPrecision -> 120, MaxRecursion -> 100, PrecisionGoal -> 110]

%Y Cf. A263136, A263177.

%K nonn,cons

%O 0,2

%A _Vaclav Kotesovec_, Oct 11 2015