Ray,
You are absolutely right, I made ??a mistake.
My reply to your message is still being verified by a moderator. There
are many formulas that I wrote on a sheet of paper and scanned. I
decided that it's faster than typing a formula in text mode. Now we
await the decision of moderator.
By the way, why did you decide to use to communicate such a strange way
of a mailing list? Why is not the forum? It would be much easier.
03.06.2012 17:38, Raymond Toy ?????:
> On 6/3/12 6:35 AM, Evgeniy Maevskiy wrote:
>> r:integrate(sin(a*x^3)/x,x);
>> =>
>> -(%i*gamma_incomplete(0,%i*a*x^3)-%i*gamma_incomplete(0,-%i*a*x^3))/6
>>
>> What is gamma_incomplete(0,z) where z in C ?
>>
>> limit(r,x,inf);
>> =>
>> 0
>>
>> This is wrong.
>
> Why is this wrong? From http://functions.wolfram.com/06.06.06.0014.01,
> we have the asymptotic series
>
> gamma_incomplete(a,z) ~ exp(-z)*z^(a-1)*(1+O(1/z))
>
> Then gamma_incomplete(0,%i*a*x^3) ~ exp(-%i*a*x^3)/(%i*a*x^3)
>
> So |gamma_incomplete(0,%i*a*x^3)| ~ 1/a/x^3 -> 0 as x -> inf. (For real a.)
>
> Did I make a mistake here?
>
> Ray