Next: The Mean When a
Up: Calculation of the Mean
Previous: The Mean When a=0
The Mean When a Is Rational
Now we no longer assume a to be 0 and return to equation (10) for X_{n,a}:

(38) 
A little thought shows that in general,

(39) 
for any real numbers x and y. Applying (39) to the first term in
(38) gives

(40) 
and so
X_{n,a} 
= 

(41) 

= 

(42) 
Thus, the number of eigenvalues X_{n,a} in the interval
20000925