Trigonometric definite integral resulting in sinc-likefunction



On Thu, 15 Jul 2010, Richard Hennessy wrote:

> "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);

OK, but the algebraic expression is still a correct value of the
integral - it's at the substituion of m = 0 stage that things go wrong
in the above, no?

> (%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.

Indeed it would.  I know asksign is deeply unpopular, but... ;-).

-- 

Regards,

Dan