Trigonometric definite integral resulting in sinc-likefunction

"which is correct for all real m."  Actually this is not exactly true.

(%i1) sin(2*%pi*%m)/(2*%pi*m),m=0;
Division by 0
 -- an error. To debug this try: debugmode(true);

(%i2) integrate(cos(2*%pi*m*x),x,0,1),m=0;
(out2) 1

This type of answer could be made correct for all m but it would complicate many results.

Rich


--------------------------------------------------
From: "Dan" <vi5u0-maxima at yahoo.co.uk>
Sent: Thursday, July 15, 2010 8:22 AM
To: "Maxima mailing list" <maxima at math.utexas.edu>
Subject: Trigonometric definite integral resulting in sinc-likefunction

> 
> Dear All,
> 
> If I do
> 
> integrate(cos(2*%pi*m*x),x,0,1) ;
> 
> I get back an answer
> 
> sin(2*%pi*%m)/(2*%pi*m)
> 
> which is correct for all real m.  However, if I do
> 
> declare(m,integer) ;
> integrate(cos(2*%pi*m*x),x,0,1) ;
> 
> I get back an answer
> 
> 0
> 
> which is not correct for all integer m (it's wrong for m = 0).
> 
> Any comments, please?
> 
> -- 
> 
> Regards,
> 
> Dan
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