Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
x_x [2016/04/05 09:33] nikolaj |
x_x [2020/01/10 23:08] nikolaj |
||
|---|---|---|---|
| Line 17: | Line 17: | ||
| Furthermore | Furthermore | ||
| - | ^ $x^x = x \sum_{n=0}^\infty \prod_{k=1}^n (1-x)\left(1-\frac{1+x}{k}\right) = x \sum_{n=0}^\infty \frac{1}{n!}(1-x)_n(1-x)^n $ ^ | + | ^ $x^x = \sum_{n=0}^\infty \prod_{k=1}^n (1-x)\left(1-\frac{1+x}{k}\right) = \sum_{n=0}^\infty \frac{1}{n!}(1-x)_n(1-x)^n $ ^ |
| with the Pochhammer symbol $(1-x)_n:=\prod_{k=0}^{n-1} (k-x)=\prod_{k=1}^n (k-(1+x))$. | with the Pochhammer symbol $(1-x)_n:=\prod_{k=0}^{n-1} (k-x)=\prod_{k=1}^n (k-(1+x))$. | ||
