Re: Limit doesn't work properly

*To*: mathgroup at smc.vnet.net*Subject*: [mg13247] Re: [mg13184] Limit doesn't work properly*From*: David Withoff <withoff>*Date*: Fri, 17 Jul 1998 03:17:43 -0400*Sender*: owner-wri-mathgroup at wolfram.com

> Hello, > > Mathematica doesn't find the correct result as a number (1/e) of the > following sequence: > > a[v_]:=v!/v^v; > N[Limit[a[v+1]/a[v],v->Identity]; > > What is the reason for this circumstance ?? > > Alex When you evaluate this limit, you should get warning messages about the essential singularity. The built-in Limit function is based primarily on power series expansions, and so is not currently programmed to handle limits at essential singularities. The algorithm used by the Calculus`Limit` package is designed to handle limits at essential singularities: In[1]:= a[v_]:=v!/v^v In[2]:= << Calculus`Limit` In[3]:= Limit[a[v+1]/a[v],v->Infinity] 1 Out[3]= - E As has already been discussed in a separate thread, the Calculus`Limit` package is not designed for general use, as it has a number of known deficiences (which is the main reason that it is not the default function). It is included because it happens to be useful for certain limits, such as this one, that are not handled by the built-in Limit function. The best of both functions will probably be incorporated into the same function for a future version of Mathematica. Dave Withoff Wolfram Research