### Theorem F

* There is a positive constant such that*
* where is the constant defined in Theorem D.*

### Proof F

Suppose .
Then
where
and and
.
Now Theorem D shows that
and Theorem E shows that
where and
is a constant by Theorem C.
Now
using the binomial theorem and Stirling's formula.
Hence
Then this inequality and (2.22) imply (2.21) with
.