I must show, using integration by parts that for all positive . I've tried but I don't get the result. The fact that the integral is dt and that the function depends of x is responsible of my fail.

Can you start me up?

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- Jun 23rd 2008, 01:56 PMarbolis[SOLVED] Gamma function simple help needed
I must show, using integration by parts that for all positive . I've tried but I don't get the result. The fact that the integral is dt and that the function depends of x is responsible of my fail.

Can you start me up? - Jun 23rd 2008, 02:03 PMMathstud28
- Jun 23rd 2008, 02:12 PMarbolisQuote:

Let http://www.mathhelpforum.com/math-he...df758ac9-1.gif

and http://www.mathhelpforum.com/math-he...4ceb1786-1.gif

Now notice that your first term dissapears.

- Jun 23rd 2008, 02:14 PMgalactus

Let

Then we get:

- Jun 23rd 2008, 02:17 PMMathstud28
- Jun 23rd 2008, 02:22 PMarbolis
Oh, thanks to both. Now I got it!! But

**I don't understand one thing**.

With , du is the derivative of u, right? u equals to , so the derivative equals . How do you get to ? - Jun 23rd 2008, 02:30 PMo_O
You're integrating with respect to t so treat x as a real number:

Also, using your method:

-- Totally would've answered this thread but too slow .. Gamma ftw! - Jun 23rd 2008, 02:31 PMMoo
Hello !

You have to be very careful :)

The notation that is used is not*that*right.

You should say that u is a function of t.

So this is ,__not__

(Wink)

I think the better way not to be confused is to take n instead of x. So that we're almost sure not to take n as a variable, since we barely use it as a variable :D - Jun 23rd 2008, 02:41 PMarbolisQuote:

You're integrating with respect to t so treat x as a real number: http://www.mathhelpforum.com/math-he...c6cbfa7d-1.gif

Also, using your method:

http://www.mathhelpforum.com/math-he...7fdfd9cf-1.gif

Quote:

You have to be very careful :)

The notation that is used is not*that*right.

You should say that u is a function of t.

So this is http://www.mathhelpforum.com/math-he...6efb4d45-1.gif,__not__http://www.mathhelpforum.com/math-he...e687d1a1-1.gif

(Wink)

I think the better way not to be confused is to take n instead of x. So that we're almost sure not to take n as a variable.

My exam of Calculus II is coming up next 21st of July, so I have all the time to fix such problems of mine. A big thanks to you. - Jun 23rd 2008, 02:46 PMMathstud28