# [Maxima] extending limit

Barton Willis willisb at unk.edu
Tue Sep 8 12:08:06 CDT 2009

```maxima-bounces at math.utexas.edu wrote on 09/08/2009 11:21:55 AM:

>
> 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.

Thanks--Maxima should have a function that *tries* to determine if an
expression is continuous on an interval--this function should be somewhat
better than the average freshman calculus student, and it should use
object-oriented function dispatch so that it can be extended without
appending more cases to a conditional. Such a function would be useful for

integrate and limit.

Barton

P.S. By the way, I noticed:

(%i1) limit(sin(%pi * x),x,inf);
(%o1) ind

(%i2) declare(x,integer)\$
(%i3) limit(sin(%pi * x),x,inf);
(%o3) 0

See TE 1 on page 5 of

http://www.unk.edu/uploadedFiles/facstaff/profiles/willisb/six-facts-mostly-about-sums.pdf

```

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