Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Barton Willis
Date: Sat, 17 Jul 2010 16:32:35 -0500
-----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