OUCH! I can't believe my senility. Change the subject to the Limits of my credibility. I thought I was typing Limit[ArcSinh[x Log[x] - x] - Log[Log@x]^1 - 1/E^E^E^E^E^x, x -> \[Infinity]] and that no matter how slightly I perturbed my question, the answer swung from -∞ to ∞. Rob Corless, of LambertW fame, was able to expand the LHS after loading Maple's MultiSeries. I'll send his interesting result along a minor surprise, and to WRI Support a raft of pathology. --rwg It looks like MultiSeries has most of the functionality of nhayat, but with some peculiarity. On Sun, Jul 10, 2016 at 5:28 PM, Bill Gosper <billgosper@gmail.com> wrote:
In[152]:= Limit[ArcSinh[x Log[x] - x] - Log[Log@x]^1, x -> \[Infinity]]
Out[152]= -\[Infinity]
In[167]:= Limit[ArcSinh[x Log[x] - x] - Log[Log@x]^(1 - 1/E^E^E^E^E^x), x -> \[Infinity]]
Out[167]= \[Infinity]
There was a brief shining moment when developmental Macsyma could actually do these, using Bill Dubuque's nhayat asymptotic expansion system, inspired by a certain moderator. --rwg