# [Maxima] extending limit

Richard Fateman fateman at cs.berkeley.edu
Tue Sep 8 11:42:59 CDT 2009

I've been critical of Mathematica's use of Intervals  for the result of
Limit, but perhaps we could come up with something similar.

Mathematica says this..

Limit[Sin[x],x->Infinity]    is  Interval[{-1,1}]

this,  but I would not mind a notion of a limit set or constraint or
something like that.

e.g.  limit(sin(x),x,inf)  might be  bounds(-1,1).

To some extent  bounds(a,b) can be handled arithmetically like an
interval   (which Maxima does not have now anyway!)
but it fails to satisfy the epsilon-delta kind of definition of limit,
or consequences that follow from that. But I have not
fully thought this through.
RJF

Limit[Tan[x]^2+Sec[x]^2,x->Infinity]

Raymond Toy wrote:
> Barton Willis wrote:
>
>> I was playing with the idea of appending a simplim%function for the
>> hypergeometric
>> functions. To start, I wrote some 100% fake code:
>>
>>
>>
> [snip]
>
>> Limit assumes continuity?
>>
>>   (%i14) limit(hypergeometric([a],[b],x),x,0);
>>   (%o14) 1
>>
>> Limit doesn't even try limit-hg?
>>
>>   (%i16) limit(hypergeometric([a],[b],x),a,0);
>>   (%o16) limit(hypergeometric([a],[b],x),a,0)
>>
>>
>>
> This is caused by the following in simplimit:
>
> (defmfun simplimit (exp var val &aux op)
>   (cond
>     ((eq var exp) val)
>     ((or (atom exp) (mnump exp)) exp)
>     ((and (not (infinityp val))
>       ;; *** HERE ***
>       (not (amongl '(%sin %cos %atanh %cosh %sinh %tanh mfactorial %log)
>                exp))
>       (not (inf-typep exp))
>       (simplimsubst val exp)))
>
> Since hypergeometric isn't among the list of "special" functions,
> simplimsubst is called.
>
> This looks like a bug in simplimit.  The list of special functions needs
> to expanded.  Or probably better, it should be removed and the rest of
> the code adjusted accordingly so that the special limit functions can
> decide what to do about continuity and such.
>
> Ray
>
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