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| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
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euler_beta_function [2015/01/13 13:14] nikolaj |
euler_beta_function [2015/01/13 13:17] nikolaj |
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| For natural numbers | For natural numbers | ||
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| - | * $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ | ||
| * ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ | * ${\large{n \choose k}}=(n+1)\cdot\dfrac{1}{{\mathrm B}(n-k+1,k+1)}$ | ||
| + | |||
| + | * $\dfrac{1}{{\mathrm B}(x,y)} = \frac{x\,y}{x+y} \prod_{n=1}^\infty \left( 1 + \dfrac{x\,y}{n\,(x+y+n)}\right)$ | ||
| === Reference === | === Reference === | ||
