# Finding non trivial sum

1. May 18, 2012

### Jakim

Hi. I tried to evaluate a definite integral of $x^x$ from $0$ to $1$ and I have reached following sum:

$$\int_0^1 x^x = \sum_{n=1}^{\infty} \frac{(-n)^{1-n}}{n}$$

Is there an expression of this sum, for example in terms of Meijer G-function? I tried to find $x^x$ as G-function form to integrate it but unsuccessful.

2. May 18, 2012

### Citan Uzuki

I'm not sure whether it's related to the G-function or not, but the sum itself is well-known, and is called the Sophomore's dream.

3. May 18, 2012

### Jakim

Thanks, I didn't know it has a name; I will look for articles about it. Anyway I have reached the sum the same way as it is shown in your link.

4. May 20, 2012

### JJacquelin

5. May 20, 2012