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euler_beta_function [2015/01/13 13:09] nikolaj |
euler_beta_function [2015/01/13 13:14] nikolaj |
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| For natural numbers | For natural numbers | ||
| - | $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ | + | * $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ |
| - | ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ | + | * ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ |
| === Reference === | === Reference === | ||
