Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
|
factorial_function [2015/11/14 03:08] nikolaj |
factorial_function [2015/11/14 03:33] ben |
||
|---|---|---|---|
| Line 8: | Line 8: | ||
| === Discussion === | === Discussion === | ||
| - | Thinking of $n!=\frac{{\mathrm d}^n}{{\mathrm d}x}x^n$ and Fermat theory, I though there must be an expression for $n!$ which is more algebraic and indeed I found | + | Thinking of $n!=\left.\frac{{\mathrm d}^n}{{\mathrm d}x^n}\right|_{x=0}x^n$ and Fermat theory, I though there must be an expression for $n!$ which is more algebraic and indeed I found |
| <code> | <code> | ||
| Line 29: | Line 29: | ||
| The binomial coefficients use the factorial of course, so there's not real computational benefit. | The binomial coefficients use the factorial of course, so there's not real computational benefit. | ||
| + | |||
| + | The theorem underlying here is that, for all $n$ | ||
| + | |||
| + | $\sum_{k=0}^n\dfrac{(-1)^k (-k)^n}{k!\,(n - k)!}=1$ | ||
| ----- | ----- | ||
