Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Stavros Macrakis
Date: Sat, 17 Jul 2010 19:08:30 -0400
If the singularity isn't removable, then of course you need some other
approach....
On Sat, Jul 17, 2010 at 17:32, Barton Willis <willisb at unk.edu> wrote:
> -----macrakis at gmail.com wrote: -----
>
> >Rather than say that the result of integrate(cos(a*x),x) should be (if a=0
> >then x else sin(a*x)/a), I would prefer to say that the Maxima expression
> >sin(a*x)/a denotes the function defined by that expression when a<>0 and
> >its analytical continuation when a=0.
>
> >The problem with that of course is that 'subst' doesn't work that way.
> >There are two solutions to that: 1) to keep subst as it is, and say that
> >it has a strictly syntactic interpretation of expressions (which is true);
> >2) to make subst essentially a synonym for limit.
>
> That works for many functions, but how about:
>
> (%i96) load(abs_integrate)$
> (%i99) subst(x=3/2, integrate(floor(m*x),x))$
>
> (%i100) [limit(%,m,0,'minus), limit(%,m,0,'plus)];
> (%o100) [-3/2,0]
>
> The expression %o99 has a nonremovable singularity at 0. Other than a
> conditional expression (or an asksign), what is the workaround?
>
> --Barton
>