- Thread starter
- #1

#### Also sprach Zarathustra

##### Member

- Jan 31, 2012

- 54

A little problem:

With the given series,

$$Y(x)= \sum_{n=1}^{\infty}(-1)^n\frac{x^n\ln^nx}{n!} $$ ,

why $Y(x)$ is Uniformly converges for all $x\in(0,1]$ ?

Ok, I know that $Y(x)$ is u.c by M-test:

$$\max{|x\ln{x}|}=\frac{1}{e}$$

And,

$$ \sum_{n=0}^{\infty}\frac{(\frac{1}{e})^n}{n!} $$

Is converges! But why only in $(0,1]$ ?

Thank you!