[Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result

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Bugs item #3105512, was opened at 2010-11-08 21:22
Message generated for change (Comment added) made by giniu
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Category: Lisp Core - Integration
Group: None
Status: Pending
Resolution: Works For Me
Priority: 5
Private: No
Submitted By: Andrzej Giniewicz (giniu)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result

Initial Comment:
integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by  \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1.

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Comment By: Andrzej Giniewicz (giniu)
Date: 2010-11-08 22:40

Message:
Indeed, I missed it I tested the diff on older version. Anyway, what is the
reason for the difference in form of result in integrating (s^2 * exp(-
(a+b) * s^2 )); and (s^2 * exp(- a * s^2 ));?

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Comment By: Dieter Kaiser (crategus)
Date: 2010-11-08 22:04

Message:
I do not see a real problem, because we can verify the following:

(%i1) (s^2 * exp(- (a+b) * s^2 ));
(%o1) s^2*%e^((-b-a)*s^2)

(%i2) integrate(%,s);
(%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s))

(%i3) diff(%,s);
(%o3) s^2*%e^-((b+a)*s^2)

We get back the integrand. I have compared the result with a result from
Wolfram alpha. It is possible to expand the integral in terms of the erf
function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2).
That is the result of this bug report too. But this is not an error. The
result might be not the expected result, but it is not wrong.

Setting the status to pending and the resolution to "works for me".
Dieter Kaiser

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