- status: open --> pending
Good day!
I have problem with my Maxima:
build_info()$
Maxima version: 5.16.2
Maxima build date: 7:44 8/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8
When I integrate romberg(sin(x)^3,x,0,2*%pi) I get error:
`romberg' failed to converge
-- an error. To debug this try debugmode(true);
And if power is 5,7 and so on.
What's wrong?
There have been related reports in the past. romberg tries to find a numerical solution, but is not always succesful. There are better routines like the quadpack functions to do a numerical integration. There is nothing wrong with the implementation. It is a weakness of the romberg algorithm.
Maxima can calculate an exact definite integral for the function of this bug report and the more general function sin(x)^n, with n a positive integer. The results are:
(%i1) declare(n,odd)$
(%i2) assume(n>0)$
(%i3) integrate(sin(x)^n,x,0,2*%pi);
(%o3) 0
(%i4) declare(k,even)$
(%i5) assume(k>0)$
(%i6) integrate(sin(x)^k,x,0,2*%pi);
(%o6) 2*beta(1/2,(k+1)/2)
Setting this bug report to "won't fix" and the status to pending.
Dieter Kaiser
Well, the problem with this integral is that it is exactly zero, which makes it difficult for any numerical method. (quad_qags returns approx 1e-17 and prints a warning message.)
Agreed that we won't try to fix it, but it's not just a weakness in romberg.
This Tracker item was closed automatically by the system. It was
previously set to a Pending status, and the original submitter
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