I have been trying to evaluate the following series in GP:
sum(x=1,x^x/(factorial(x)*exp(x))-(2*Pi*x)^-0.5)
The sum should converge (very slowly) to -0.084069508727655... ( -2/3-zeta(1/2)/sqrt(2*Pi))
but I cannot get more than the first two decimal places however I try to rearrange and split the series terms. Is there any way I can quickly get more digits, say to 20 places? Any help at all would be highly appreciated.
Thank you.
Lucas