Is $\sum_{n=0}^\infty\frac{(x\ln x)^n}{n!}$ a power series?

Question

Why this is a power series?

$$\sum_{n=0}^\infty\frac{(x\ln x)^n}{n!}$$

The power series is like $$\sum_{n=0}^\infty C_n(x-a) ^n$$

Thank you for your help!

Answer 1

Strictly speaking, it is not a power series. Anyway it is a power series in terms of $x\ln x$. Needless to say, it converges to $x^x$.

Answer 2

No. You already explained what a power series is. This is not a power series.