Math Help - integral function!

1. integral function!

show that
$B(x,y)= B(x+y,3)$

i tried to solve the problem as follows

$\frac{\Gamma{x+y} \Gamma{3}}{\Gamma{x+y+3}}$

can of confuse here on how to go forward, pls i need help here.

thanks

2. Re: integral function!

B(x, y) is the beta function, [tex]B(x, y)= \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+ y)}, right?
So $B(x+ y, 3)= \frac{\Gamma(x+ y)\Gamma(3)}{\Gamma(x+ y+ 3)}$
(You need some parentheses to clarify what you are writing!)
That is what you have. Now, can you use the fact $\Gamma(x)= \int_0^\infty t^{x- 1}e^{-xt}dt$, with some substitutions,
to show that?