# [Maxima] limit of erfc

Stavros Macrakis macrakis at alum.mit.edu
Thu May 17 14:23:44 CDT 2012

```Currently, atan(inf) => %pi/2, but normally you need to apply 1-argument
limit:

exp(inf) => exp(inf)
limit(exp(inf)) => inf

atan(inf^2) => atan(inf^2)
limit(atan(inf^2)) => %pi/2

atan(inf) => inf can get you in to trouble:

(atan(inf)-%pi/2)*inf => 0
but
limit(atan(x)-%pi/2)*x,x,inf) => -1

-s

On Thu, May 17, 2012 at 2:54 PM, Rupert Swarbrick <rswarbrick at gmail.com>wrote:

> Raymond Toy <toy.raymond at gmail.com> writes:
> > I noticed when running just the rtest_gamma test, I get two failures:
> > limit(erfc(z),z,inf) and limit(erfc(z),z,minf).  This doesn't happen
> when I
> > run the entire testsuite.  I guess something is leaking into rtest_gamma
> > from earlier tests.
> >
> > However, from a fresh maxima session, maxima cannot determine
> > limit(erfc(z),z,inf).  But maxima knows limit(erf(z),z,inf) = 1.
> >
> > Also, erf(inf) -> 1, erfc(inf) -> 0, erf(minf) -> -1, erfc(minf) -> 2.
>  Why
> > is that?  Compare what happens with tanh(inf) which just returns the noun
> > form.  Also, sinh(inf) -> sinh(inf).
>
> Hmm, that's interesting. Are there many functions in Maxima that
> simplify to numbers when given inf or minf? What I remember from
> undergraduate analysis is screaming that f(inf) is pretty much always
> nonsense, but maybe there's a convention to use that sort of thing in
> other fields?  Physics?  Engineering? I presume that one just defines
> that
>
>  f(inf) = lim(f(x), x, inf);  ?
>
> I suppose that, since we distinguish inf from infinity, we don't have to
> worry about 1 point vs 2 point compactifications of R.
>
> I notice that log(inf) just yields log(inf) (rather than inf). Should we
> try to make this feature more uniform?
>
> Rupert
>
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