[Maxima-bugs] [ maxima-Bugs-887646 ] bogus PV integral [defint(exp(a*x), x, 0, inf)]

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Bugs item #887646, was opened at 2004-01-30 15:49
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: bogus PV integral [defint(exp(a*x),x,0,inf)]

Initial Comment:
(C1) defint(exp(a*x),x,0,inf);
Is  a  positive, negative, or zero?

zero;Principal Value
(D1) 				       0

This isn't a PV integral; the integral diverges when 
a == 0.


(C2) build_info();

Maxima version: 5.9.0
Maxima build date: 19:10 2/9/2003
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL-2-5.0 



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>Comment By: Dieter Kaiser (crategus)
Date: 2009-05-27 02:08

Message:
The behavior has changed:

The sign of a is unknown. Maxima returns a noun form:

(%i3) defint(exp(a*x),x,0,inf);
(%o3) 'integrate(%e^(a*x),x,0,inf)

The sign of a is negative. We get the correct solution:

(%i4) assume(a<0)$

(%i5) defint(exp(a*x),x,0,inf);
(%o5) -1/a

The sign of the parameter b is positive. The integral is divergent:

(%i6) assume(b>0)$

(%i7) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
 -- an error.  To debug this try debugmode(true);

Up to here the solutions are correct and consistent. We assume a paramter
less or equal zero and get a divergent result. I think, this should give a
noun form too:

(%i10) forget(a<0)$
(%i11) assume(a<=0)$

(%i12) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
 -- an error.  To debug this try debugmode(true);

This is again correct. The integral is divergent when b is greater or
equal zero:

(%i13) forget(b>0)$
(%i14) assume(b>=0)$

(%i15) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
 -- an error.  To debug this try debugmode(true);

Perhaps we can change the one open case for a parameter a<=0. Then all
cases will be correct.

Dieter Kaiser

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Comment By: Harald Geyer (hgeyer)
Date: 2008-03-25 04:00

Message:
Logged In: YES 
user_id=929336
Originator: NO

Still observed in 5.14.0 and cvs HEAD from 2008-03-25

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