The Homotopy Derivative



Casey Coleman <junglejesus93 at gmail.com> writes:
> So how about those sums? Is there a way to express an unknown infinite
> sum in an algebraically useful way in Maxima?

You mean like say "Right, a(n) is going to represent the (unknown) n'th
term in my series"? Yep. You just call it a(n)... There's no reason you
have to define it in advance.

> Maybe think in these terms: Let y and z be power series in q.
> D(m, y*z) := block(
>     step one: calculate the resultant series out to order m
>     step two: choose the coefficient of q^m and return it (simplified)
> );
>
> Damn, that's actually a pretty good start...any thoughts at all would
> be greatly appreciated.

Ok, well if you do this you should ignore my previous comment and make
sure you use Maxima's memoizing a[n] functionality. Otherwise, this
approach will be very inefficient.


Rupert
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