Euler beta function
Function
| definition | B:{z | R(z)>0}2→C |
| definition | B(p,q):=∫10τp−1(1−τ)q−1dτ |
Theorems
For natural numbers
- {\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
Wikipedia: Beta function
Subset of
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