Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Dan
Date: Thu, 15 Jul 2010 23:57:31 +0100 (BST)
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