# integral function!

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• May 13th 2013, 06:37 AM
lawochekel
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
• May 13th 2013, 09:27 AM
HallsofIvy
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?