I should not have used the abs() function. This is a simpler answer and it
does not blow up at zero.
(gamma(1/4)/4-gamma_incomplete(1/4,x^4)/4)*signum(x);
Don't drink and drive. Happy New Year,
Rich
-----Original Message-----
From: Richard Hennessy
Sent: Saturday, December 31, 2011 7:17 PM
To: Maxima List
Cc: Barton Willis
Subject: Re: [Maxima] Bug in limit or integrate
I get for the answer the following function.
integrate(exp(-x^4),x);
-((gamma_incomplete(1/4,x^4)-gamma(1/4))*abs(x)-gamma(1/4)*x)/(4*x)
I checked this out. Looks right to me. Wolfram alpha disagrees with me but
I think they got it wrong too. Maple expresses the answer in term of the
WhittakarM function which I have not checked out.
Rich
-----Original Message-----
From: Richard Hennessy
Sent: Saturday, December 31, 2011 6:54 PM
To: Barton Willis
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Bug in limit or integrate
The indefinite integral of a continuous function which is finite valued on a
region (a,b) is also continuous on the region (a,b). Check it out. The
answer for this indefinite integral is wrong since it is discontinuous at
zero. If I can figure out the right answer I will post it.
Rich
-----Original Message-----
From: Barton Willis
Sent: Saturday, December 31, 2011 8:57 AM
To: rich.hennessy at verizon.net
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Bug in limit or integrate
The function x |-> -gamma_incomplete(1/4,x^4)*x/(4*abs(x)) is not
continuous at zero. To do
the calculation correctly, you need to consider the intervals (-inf,0) and
(0, inf) separately.
Doing that, the definite integral is correct, I think.
Sometime ago, I wrote a bit of code that attempts to determine when an
expression is continuous. I know
that in general this is algorithmically impossible--I was aiming for a
satisficing (good enough) method.
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
I get this incorrect result for the following calculations:
(%i4) kill(all);
(%o0) done
(%i1) exp(-x^4);
(%o1) %e^-x^4
(%i2) integrate(%o1,x,minf,inf);
(%o2) gamma(1/4)/2
(%i3) integrate(%o1,x);
(%o3) -gamma_incomplete(1/4,x^4)*x/(4*abs(x))
(%i4) limit(%o3,x,inf)-limit(%o3,x,minf);
(%o4) 0
The limit should give the same answer as the more direct definite integral.
I can’t take the analysis much further because I know very little
about the gamma_incomplete function. It looks like a bug.
Rich
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