Beta and gamma functions

**roshanhero** · October 6th 2008, 10:44 PM

Prove that
Г(n+1)=nГ(n)
I am totally confused with it,so please help me through this...........

**shawsend** · October 7th 2008, 12:58 AM

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 $s\Gamma(s)$

**roshanhero** · October 9th 2008, 05:06 AM

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

**p00ndawg** · October 9th 2008, 05:12 AM

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.

**shawsend** · October 9th 2008, 07:26 AM

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 $s\Gamma(s)$ .

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