# [Maxima] limit of erfc

Stavros Macrakis macrakis at alum.mit.edu
Thu May 17 15:02:54 CDT 2012

```On Thu, May 17, 2012 at 3:50 PM, Raymond Toy <toy.raymond at gmail.com> wrote:
>
> On Thu, May 17, 2012 at 12:23 PM, Stavros Macrakis <macrakis at alum.mit.edu>wrote:
>
>> 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:
>>
>
> Presumably you meant %pi/2, not inf.
>

Yes.

>
>>         (atan(inf)-%pi/2)*inf => 0
>> but
>>         limit(atan(x)-%pi/2)*x,x,inf) => -1
>>
>>
> I take this to mean we shouldn't have atan(inf) -> %pi/2.  Which means
> erf(inf) and friends should just return a noun.  But 0*inf always returns
> 0. Shouldn't we return und for that?
>

We should either return und or leave it unsimplified.  Similarly for
inf-inf, inf^0, is(equal(inf,inf)), etc. which currently return nonsense
results.

I believe someone shared code for this on the list, but it hasn't been
integrated.  Not sure why.  Is it incomplete? Buggy?  Does it slow down
simplification too much?

-s

> A peek at the code shows that simp-erf has special tests for this.  These
> should probably be removed, then.
>
> Ra
> y
>
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