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