Re: [Maxima-discuss] definite integration of power series

[Raymond T. <toy...@gm...>]

>>>>> "Barton" == Barton Willis <wi...@un...> writes:

    Barton> My workaround is manual termwise integrate (extract
    Barton> summand, integrate, ...). Declare integration to be linear
    Barton> doesn't work--defint thinks all definite integrals of
    Barton> infinite sums diverge, I think.

    Barton> (%i6) declare(integrate,linear);
    Barton> (%o6) done

    Barton> OK:

    Barton> (%i7) integrate(sum(x^k/k!,k,0,inf),x);    
    Barton> (%o7) sum(x^(k+1)/((k+1)*k!),k,0,inf)

    Barton> Bogus error message (integral is convergent for all real z).

    Barton> (%i8) integrate(sum(x^k/k!,k,0,inf),x,0,z);
    Barton> defint: integral is divergent.

Don't know about the message about divergence, but wouldn't maxima
kind of have to prove that the interchange of the integration and the
infinite sum is actually allowed? Like uniform convergence and so on.

Or maybe maxima doesn't normally do these checks. I can't remember.

Ray