Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Last revision Both sides next revision | ||
|
euler_beta_function [2015/01/13 13:17] nikolaj |
euler_beta_function [2015/01/13 13:17] nikolaj |
||
|---|---|---|---|
| Line 10: | Line 10: | ||
| For natural numbers | For natural numbers | ||
| - | * $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ | ||
| * ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ | * ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ | ||
| + | |||
| + | * $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ | ||
| === Reference === | === Reference === | ||
