70 TEMPORAL ORGANIZATION IN CELLS 



For the other phase integral we have 



Z,.. = J e-^"'^^ 



,— log d+j',)] 



dy 





-T« 



Now write 17 = ^6,(1 +>',■). At 



The integral is thus reduced to 



AiPbdQi 



where 



00 



(35) 



the incomplete gamma function. 



It will be important in the following to obtain expressions for these phase 

 integrals in the hmits of large and small /S. For Zp. we use the results 



[-'. 



Erfc\-p,li^^] 



V 



TT 



2 



asi3->0 



as /? -5^ 00 



Hence from equation (34) we readily get the limits 



'■AM '-« 



'27t\ 



i3 



CO 



(36) 



Since r(l,0) = 1, we get for Z,,, in the limit of small j8 



/ 1 \^b>+\ 





^^0 



(37) 



