#2686 Integral of sin(n*%pi*x)*sin(m*%pi*x) leads incorrect result

[Markus Fenske]

Maxima should return delta(n,m)*1/2 instead of 0, because of n=m, then the integral is 1/2.

I am running the following version:

Maxima version: "5.30.0"
Maxima build date: "2013-06-05 12:29:41"
Host type: "x86_64-redhat-linux-gnu"
Lisp implementation type: "SBCL"
Lisp implementation version: "1.1.8-2.fc19"

Console output is this:

(%i1) declare(n, integer, m, integer);
(%o1) done
(%i2) assume(n > 0, m > 0);
(%o2) [n > 0, m > 0]
(%i3) integrate(sin(n%pix)sin(m%pi*x),x,0,1);
(%o3) 0

Cheers!

[Barton Willis]

Yes, this is a bug, but there is a typo in your input:

(%i3) integrate(sin(n%pix)sin(m%pi*x),x,0,1);
(%o3) 0

Eliminating declare(n, integer, m, integer) gives

(%i3) integrate(sin(n%pix)sin(m%pix),x,0,1);
(%o3) -((n-m)sin(%pin+%pim)+(-n-m)sin(%pin-%pim))/(2%pin^2-2%pi*m^2)

This is still wrong for n=m. Thank you for posting your bug report.

[Rupert Swarbrick]

I'm closing this as a duplicate of [bugs:#2652]

Unfortunately, SF's bug system doesn't do "advanced features" like marking bugs as duplicates, so I'm going to just close this bug and leave a corresponding link in the other one. :-(