[Maxima-bugs] [ maxima-Bugs-3311145 ] integrate(x^m * exp(-x^2), x, minf, inf) --> 0

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Bugs item #3311145, was opened at 2011-06-03 18:58
Message generated for change (Comment added) made by aleksasd
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary:  integrate(x^m * exp(-x^2),x,minf,inf) --> 0

Initial Comment:
Bogus:

(%i1) integrate(x^m * exp(-x^2),x,minf,inf);
"Is  "m+1"  positive, negative, or zero?"pos;
"Is "m" an "integer"?"yes;
(%o1) 0

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Comment By: Aleksas (aleksasd)
Date: 2011-06-14 15:58

Message:
All correct:

(%i1) kill(all)$
(%i1) declare(m,even); assume(m+1>0);
(%o1) done
(%o2) [m>-1]
(%i3) integrate(x^m * exp(-x^2),x,minf,inf);
(%o3) gamma((m+1)/2)

(%i4) kill(all)$
(%i1) declare(m,odd); assume(m+1>0);
(%o1) done
(%o2) [m>-1]
(%i3) integrate(x^m * exp(-x^2),x,minf,inf);
(%o3) 0

(%i4) kill(all)$
(%i1) integrate(x^(-1) * exp(-x^2),x,minf,inf);
Principal Value
(%o1) 0
(%i2) integrate(x^(-1) * exp(-x^2),x,0,inf);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);
(%i3) integrate(x^(-1) * exp(-x^2),x,minf,0);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);

(%i4) kill(all)$
(%i1) assume(m+1<0);
(%o1) [m<-1]
(%i2) /* Principal Value */
integrate(x^m * exp(-x^2),x,minf,inf);
(%o2) 0
(%i3) integrate(x^m * exp(-x^2),x,0,inf);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);
(%i4) integrate(x^m * exp(-x^2),x,minf,0);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);

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https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311145&group_id=4933