Re: Simple Convergence limit

Quote:

Originally Posted by

**RaisinBread** Hey, I'm trying to show that the following sequence of functions

converges uniformly on

.

To do that I'm trying to find the limit of the simple convergence of the sequence, I can easily show that the limit for the simple convergence exists by noticing that for every

,

and use the convergence of the Riemann Zeta Function. However I can't manage to what the function of the limit is.

In...

http://www.mathhelpforum.com/math-he...-i-188482.html

... it has been demonstrated that...

(1)

... where...

(2)

... being x! the so called 'factorial function'...

(3)

Now from (1) using l'Hopital rule You obtain...

(4)

Kind regards