I have a calculated data (x,f(x)) accurate to ~ 36 significant digits (x & f(x)). The data is in the range from (x=40 to 700) and I have 161 data pairs. I am trying to fit this data to 1/x + 1/x^2 + 1/x^3 + 1/x^4 + Log[x]/x^5 + 1/x^5 + Log[x]/x^6 + 1/x^6 + Log[x]^2/x^7 + Log[x]/x^7 + Log[x]/x^7 + .....
Instead of being able to find the coefficient of the leading 1/x term to 36 significant digits, I am stuck with ~24 digits. I am losing 11-12 digits here!!
Yes, I have checked and rechecked and re-rechecked (many more times) the claimed 36 digit of accuracy here (and I am pretty sure about it). Anyone knows how to get a good fit or estimate of the coefficients. I tried Fit, FindFit, NonlinearModelFit, NMinimize with all the options, etc. And cannot go past that. Any help appreciated. If not, why am I getting stuck at ~24 digits of precision? There has to be some explanation.