# Math Help - Beta and gamma functions

1. ## Beta and gamma functions

Prove that
Г(n+1)=nГ(n)

2. If $\Gamma(s)=\int_0^{\infty} e^{-t}t^{s-1}dt$ then $\Gamma(1+s)=\int_0^{\infty} e^{-t}t^s dt;\quad \text{Re}(s)>0$

I can now integrate that last integral by parts and express the results as $s\Gamma(s)$

3. After that what,can I have a detail explanation here pls...............

4. Originally Posted by roshanhero
After that what,can I have a detail explanation here pls...............

what are you asking? If you're asking how he got that, he used the definition of what a gamma function is.

The last integral that he left for you to do, you need to integrate it by parts, and from the looks of it its going to take you awhile.

5. Originally Posted by roshanhero
After that what,can I have a detail explanation here pls...............
Just integrate by parts the expression:

$\int_0^{\infty}e^{-t}t^{s}dt$

Just let s be an integer for now.

Let $u=e^{-t};\quad dv=t^{s}$

Now, try and finish that and you should end up with an expression that can be put into the form $s\Gamma(s)$.