7. STATISTICAL PROPERTIES OF THE EPIGENETIC SYSTEM 105 



Taking u = I o I ^ 



we get the approximation 



00 



2 \l/2 f / O-vl 2 



fe) J ^'— -£)■ 



Q-cis--:2^ 



-(Pcil2yrpi 



Returning now to the double integral, we have for large j8 



-Pi V -00 



where Rl signifies the real part of the integral. 

 Now for large ^ we know that 



-'■ ^ M 



so that we get the further reduction 



00 /^ °° a 



|l,,le-^-...v,.Ri|y-)"Ji::f^</.| 



-Pi 

 Using the known result 



00 



I 



ax = 



•^2 2 



— 00 



we get, with a = cjl^ 



-Pi 



From equation (53) we now have the expression 



co(yi-v) 



Substituting for the approximate values of Z,,. and Z^. for very large j8 we have 



CO 



(y-^) 



^VUJvUJ 



277 



