But for integrate(sin(x)/x,x); we have
-(%i*gamma_incomplete(0,%i*x)-%i*gamma_incomplete(0,-%i*x))/2
and then - correct result
integrate(sin(x)/x,x,0,inf);
=>
%pi/2
I do not understand what's going on here. Maybe someone can explain?
03.06.2012 16:35, Evgeniy Maevskiy ?????:
> 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.
>
> limit(gamma_incomplete(0,-%i*t),t,inf);
> =>
> gamma_incomplete(0,infinity)
>
> Wrong, because gamma_incomplete(0,infinity) not exists. This problem
> entails
>
> limit(gamma_incomplete(0,%i*t),t,inf)-limit(gamma_incomplete(0,-%i*t),t,inf);
>
> =>
> 0
>
> 02.06.2012 0:39, ?????? ??????? ?????:
>> integrate(sin(a*x^3)/x, x, 0, +inf);
>> maxima result: 0;
>> correct result: %pi * abs(a) / 6 / a;