`[<<][math][>>][..]`
Wed Mar 13 11:52:32 EDT 2013

## Composition of series expansion

```Is it actually possible to write this in a finite way?  E.g.

exp(exp(x)) = sum_n 1/n! (sum_m 1/m! x^m) ^n

what is the coefficient of 1, x, x^2, ... ?

Hmm... I'm missing an important point here.  The trouble is that this
is doubly infinite, so when doing this numerically, it is necessary to

Only in the first coefficient though, meaning f(0), as it will show up
as an infinite sum.  All other sums will be finite.

Finding the contribution for x^n depends on all possible splits of the
factorization of n, but is finite.

Another problem: the infinite sum might not even converge!
Actually, this is mentioned here[1] on composition g(f(X))

A point here is that this operation is only valid when f(X) has no
constant term, so that the series for g(f(X)) converges in the
topology of R[[X]]. In other words, each cn depends on only a finite
number of coefficients of f(X) and g(X).

[1] http://en.wikipedia.org/wiki/Formal_power_series#Composition_of_series

```
`[Reply][About]`
`[<<][math][>>][..]`