Trigonometric definite integral resulting insinc-likefunction

"Other than a conditional expression (or an asksign), what is the workaround?"

There is none that I know of but I don't like asksign.




From: Stavros Macrakis 
Sent: Saturday, July 17, 2010 7:08 PM
To: Barton Willis 
Cc: Maxima mailing list ; Robert Dodier 
Subject: Re: [Maxima] Trigonometric definite integral resulting insinc-likefunction


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





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