# Power series raised to powers

Power series raised to powers: I am looking for a way to implement a replacement using this relation explained on wikipedia and in another post here: https://math.stackexchange.com/questions/1471438/power-series-raised-to-an-exponent-where-does-wikipedia-get-this-formula

The series in infinite, otherwise I wouldn't worry about this question as truncation would manage it without too much of an issue. Essentially, when Mathematica encounters an infinite series raised to a power it should replace it with the relation

Sum[Subscript[a, k]*X^k, {k, 0, Infinity}]^n -> {Subscript[c, 0] + Sum[Subscript[c, m]*X^m, {m, 1, Infinity}],Subscript[c, 0] = Subscript[a, 0]^n, Subscript[c, m] = (1/(m*Subscript[a, 0]))*Sum[(k*n - m + k)*Subscript[a, k]*
Subscript[c, m - k], {k, 1, m}]}

• Hi Rupert. surprisingly!, I was about to ask the same question with the same reference you did years ago. This question, I suppose, is still relevant. Can you provide assistance if this has been resolved? Apr 28 at 1:34
• Unfortunately I haven't looked at this since the initial post but interestingly I may need to revisit this topic again over the next few months. If I work on it and progress I will update. May 18 at 10:26