Beta in terms of power of t over power of (1+t)
From specialfunctionswiki
Theorem
The following formula holds: $$B(x,y)=\displaystyle\int_0^{\infty} \dfrac{t^{x-1}}{(1+t)^{x+y}},$$ where $B$ denotes the beta function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.2.1$
