Invert Series to Find an - MathWorld

[eljose79]

Let be a series Sum(0,infinite)anX^n=f(x) then could it be inverted to get the an?..in fact if we set x=1/Z the series becomes

anZ^-n=Zeta transform of an so we could invert this (as seen in mathworld.com),could it be done to get the an?..thanks.

 

[shmoe]

"Zeta transform" isn't a term I've seen often, but I think it usually refers to the inverse of Mobeius inversion. Is this what you mean? If so, I don't see how it will help unless you know more information about the $$a_n$$ terms then you've indicated.

 

[HallsofIvy]

The a_n are, of course, given by the Taylor series formula:
$$\frac{1}{n!}\frac{d^nf}{dx^n}(0)$$