[Maxima-bugs] [maxima:bugs] #4339 rtest16 #538

[Robert D. <rob...@us...>]

I think the idea with the `declare(..., even)` is that the integral is zero when the exponent is an odd positive integer. It wouldn't hurt to test both odd and even, I guess. 

The test for the result being positive seems like a pretty weak test -- seems much more informative to test for a specific result. Aside from that, we could test with a variable declared even or odd, and also with specific even or odd values -- those should come out the same, of course.

I see from looking at the original bug report (https://sourceforge.net/p/maxima/bugs/2726/) that the declaration is said to be a workaround -- maybe we want to test with and, especially, without the declaration.


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**[bugs:#4339] rtest16 #538**

**Status:** open
**Group:** None
**Labels:** testsuite rtest16 
**Created:** Mon Aug 05, 2024 12:44 PM UTC by Barton Willis
**Last Updated:** Sun Aug 18, 2024 01:38 AM UTC
**Owner:** nobody


Test 538 in rtest16 is
```
/* #2726: Integrate produces wrong answer for Gaussian Moments */
(declare(m2726, even),
 block([tmp: integrate(exp(-x^2/2)/sqrt(2*%pi) * x^m2726, x, -1/4, 1/4)],
   sign (subst(m2726 = 4, tmp))));
pos$
```

First, I don't think that `m2767` should need to be declared to be even; and second, the integral diverges when `m2726 <= -1`.   I think the test should be modified to 

```
/* #2726: Integrate produces wrong answer for Gaussian Moments */
block([tmp, m2726],
   assume(m2726+1 > 0),
   tmp : integrate(exp(-x^2/2)/sqrt(2*%pi) * x^m2726, x, -1/4, 1/4),
   tmp : sign(subst(m2726 = 4, tmp)),
   forget(m2726+1 > 0),
   tmp);
```

Now Maxima 5.47 passes this test OK. But if `domain` is complex, the test will ask if `m2726` is an integer.

Actually, with Maxima 5.47, we have

```
(%i9)	integrate(exp(-x^2/2)/sqrt(2*%pi) * x^m2726, x, -1/4, 1/4);
(%o9) (-(2^(m2726/2-1/2)*(-1)^m2726*gamma_incomplete((m2726+1)/2,1/32))

 -2^(m2726/2-1/2)*gamma_incomplete((m2726+1)/2,1/32)

 +2^((m2726-1)/2)*(-1)^m2726*gamma_incomplete((m2726+1)/2,0)

 +gamma_incomplete(m2726/2+1/2,0)*2^(m2726/2-1/2))

 /(sqrt(2)*sqrt(%pi))
```
 
 The definite integral is OK, I think, but it's undefined when `m2726 <= -1`.


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