content_image/305315.jpg content_image/305314.jpg content_image/305313.jpg content_image/305311.jpg content_image/305312.jpg content_image/305310.jpg
sufficiently large p , 

p + α p where Γ ( np 2 , y ) is the complementary incomplete Gamma function (see Olver 1997, p.45) with y = ( p + α √ p ) ( n − A$_{2}$ 2 ) . Hence, for sufficiently large p, y > np/ 2 + nα √ p/ 4 , and we can continue 

<img src='content_image/305315.jpg'>

<img src='content_image/305314.jpg'>

Now, Γ ( β, γ ) ≤ e − $^{γ}$γ$^{β}$/ ( γ − β + 1) whenever β > 1 and γ > β − 1 (Olver 1997, p.70). Therefore, we have, for sufficiently large p , 

Comparing this to (51), we see that α can be chosen so that 

Further, for sufficiently large p , 

<img src='content_image/305313.jpg'>

<img src='content_image/305311.jpg'>

<img src='content_image/305312.jpg'>

where y = ( p − α √ p ) n − A$_{2}$ 2 < np 2 − αn √ p 4 . Therefore, for any positive z < np 2 and sufficiently large p, 

<img src='content_image/305310.jpg'>

