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#2788 says integral is divergent when it clearly is not

None
open
nobody
None
5
2014-10-23
2014-07-24
dan hayes
No

Claims integral divergent when it is obviously convergent and well defined.

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(a>0),integrate(integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),r,0,inf))

says integral is divergent and obviously it is NOT. Upper limit is obviously 0

(t:integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),ratsimp(subst(r=0,integrate(t,r))))

gives

-4*a/(k^4+2*a^2*k^2+a^4)

Discussion

  • Robert Dodier
    Robert Dodier
    2014-07-29

    • Description has changed:

    Diff:

    --- old
    +++ new
    @@ -7,9 +7,18 @@
     Lisp implementation type: GNU Common Lisp (GCL)
     Lisp implementation version: GCL 2.6.8
    
    +~~~~
     (assume(a>0),integrate(integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),r,0,inf)) 
    +~~~~
    
     says integral is divergent and obviously it is NOT. Upper limit is obviously 0
    
    +~~~~
     (t:integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),ratsimp(subst(r=0,integrate(t,r))))
    -gives -4*a/(k^4+2*a^2*k^2+a^4)
    +~~~~
    +
    +gives
    +
    +~~~~
    +-4*a/(k^4+2*a^2*k^2+a^4)
    +~~~~