content_image/352268.jpg content_image/352274.jpg
<img src='content_image/352268.jpg'>

This puts the maximum at x = ± √$_{a}$ for a > 0 and at x = 0 for a ≤ 0. 

Figure 2 works like figure 1 but here with the parameter a set to 1. It shows R$_{p,q}$ ( n, n/ 2 , x n 3 / $^{4}$) for z = − 9 with p = 1 − 0 . 105391 /n − 1 . 50171 /n 3 / 2 and the asymptotic ratio is given by (65), that is, e − 0 . 719718 ( x $^{4}$− 2 x $^{$^{2}$)}$. The red curve is the asymptote and the blue curves are for finite n where the larger n are closer to the asymptote. Had we set a < 0 the distributions would still be wide but with a single peak in the middle. 

## C. Peakish distributions 

If we instead choose a middle ratio of 1+ a/n then we receive a sharply peaked distribution. Say that we want n/ 2 n/ 2 

<img src='content_image/352274.jpg'>

