# [Maxima] Limit of the Logarithm function

Dieter Kaiser drdieterkaiser at web.de
Fri Aug 21 16:10:09 CDT 2009

```I think we have some problems with the limit of the logarithm function.

No problem with inf:

(%i3) limit(log(x),x,inf);
(%o3) inf

For minf Maxima returns an expression with an infinity in it.

(%i4) limit(log(x),x,minf);
(%o4) inf+%i*%pi

Interesting is the answer for infinity. The limit from both sides does
not work.

(%i5) limit(log(x),x,infinity);
sign: sign of infinity is undefined.
-- an error.  To debug this try debugmode(true);

And we get different answers for the limit from above and below.

(%i6) limit(log(x),x,infinity,plus);
(%o6) infinity
(%i7) limit(log(x),x,infinity,minus);
(%o7) infinity+%i*%pi

Furthermore the limit for ind is not simplified.

(%i8) limit(log(x),x,ind);
(%o8) log(ind)

The limit for und has no problem.

(%i9) limit(log(x),x,und);
(%o9) und

I think the code of simplimln has been designed to give the following

limit(log(x),x,minf)    -> infinity
limit(log(x),x,infinity -> infinity
limit(log(x),x,ind)     -> und

It is possible to change simplimln to get these answers.

I had a look at wolfram.functions.com. There the following definitions
for the limits are given:

limit(log(x),x,minf)     -> inf
limit(log(x),x,infinity) -> inf

Dieter Kaiser

```