On 6/2/12 4:26 PM, David Billinghurst wrote:
> On 3/06/2012 1:56 AM, Raymond Toy wrote:
>> On 6/2/12 4:32 AM, Jaime Villate wrote:
>>> On 06/02/2012 05:28 AM, Raymond Toy wrote:
>>>> On 6/1/12 6:20 PM, Robert Dodier wrote:
>>>>> On 2012-06-01, ?????? ???????<bankov_dmitrii at mail.ru> wrote:
>>>>>
>>>>>> integrate(sin(a*x^3)/x, x, 0, +inf);
>>>>>> maxima result: 0;
>>>>>> correct result: %pi * abs(a) / 6 / a;
>>>>> Thanks for this info. I confirm that it happens w/ Maxima 5.27.0.
>>>> How did you get this? I tried it with the current git version and
>>>> I get
>>>>
>>>> gamma(1/3)/6/a^(1/3)
>>>>
>>>> when a> 0.
>>>>
>>>> Looking at the code in defint.lisp, I see maxima has a special routine
>>>> (scaxn) to handle this type of integral.
>>>> integrate(sin(a*x^n),x,0,inf)
>>>> -> gamma(1/n)/a^(1/n)/n*sin(%pi/2/n).
>>>>
>>>>
>>> ??
>>> I got the most recent git master snapshot yesterday and compiled it
>>> with
>>> SBCL, CCL, GCL, CLisp and ECL
>>> and I also get the wrong 0 result
>>>
>>> Maxima branch_5_27_base_65_g08552c3_dirty http://maxima.sourceforge.net
>>> using Lisp CLISP 2.49 (2010-07-07)
>>> Distributed under the GNU Public License. See the file COPYING.
>>> Dedicated to the memory of William Schelter.
>>> The function bug_report() provides bug reporting information.
>>> (%i1) integrate(sin(a*x^3)/x, x, 0, +inf);
>>> (%o1) 0
>> Well that's interesting. On my mac with sources from just now, cmucl,
>> ccl, and clisp don't give 0. Maxima asks for the sign of a (pos) and
>> returns gamma(1/3)/6/a^(1/3), which I think is right. Which differs
>> from what the original poster said should be the correct value.
>>
>> Someone else is going to have to debug this.
>>
>> Could you check to see if scaxn is called? It is on my systems. If it
>> isn't, then that would be the problem.
>>
>> Ray
>>
>
> I think we are on different pages here :-) The integrand in question
> is sin(a*x^3)/x
Oops! I missed the division by x.
Well, then I do get zero. Looks like maxima computes the antiderivative
and substitutes the limits in. Don't know what's going wrong with that.
Ray