#2786 defint fails to detect divergent integral, and returns different results

[dan hayes]

wxMaxima version: 13.4.0
Maxima version: 5.31.1
Maxima build date: 2013-09-24 09:49:12
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

(assume(k>0,r>0),display2d:false,ldisp([integrate(r*demoivre(integrate(exp(%i*k*r*w),w,-1,1)),r,0,inf)
,integrate(r*ratsimp(demoivre(integrate(exp(%i*k*r*w),w,-1,1))),r,0,inf)]));

gives

[2*'integrate(sin(k*r),r,0,inf),     2*('integrate(sin(k*r),r,0,inf))/k]

Both expressions should have k in denominator but the first one, without using ratsimp, DOES NOT
- perhaps you can see this easier in the usual fancy display output without using
' display2d:false '

[Robert Dodier]

enclose code in four tildes before and after

[Robert Dodier]

2nd attempt to format

[Robert Dodier]

I've revised the title to reflect what I've figured out.

(1) defint (definite integral) returns 2 different results, depending on form of integrand (either with or without ratsimp). That's a bug.

(2) defint doesn't notice that the integral is divergent. This is a missed opportunity; it should be easy to determine that the integral is divergent.

I've simplified the bug a little bit:

(%i2) foo : r*(%i*(cos(k*r)-%i*sin(k*r))/(k*r)-%i*(%i*sin(k*r)+cos(k*r))/(k*r)) $
(%i3) defint (foo, r, 0, inf);
(%o3) 2*'integrate(sin(k*r),r,0,inf)
(%i4) defint (ratsimp (foo), r, 0, inf);
(%o4) 2*('integrate(sin(k*r),r,0,inf))/k

If defint can't figure out that the integral is divergent, it should return %o4 (with factor 1/k in result).

[Robert Dodier]

By the way, the indefinite integral, with or without ratsimp, is correct.

(%i6) integrate (foo, r);
(%o6) -2*cos(k*r)/k^2
(%i7) integrate (ratsimp (foo), r);
(%o7) -2*cos(k*r)/k^2