All-101 101 



Thus we get 



or 



Now if ij), be expanded into an asymptotic series and if 

 we keep only the first term in the series (for all practical 

 purposes, this amounts to neglecting the 0(e^-') terms), we 

 have 



^ _ tIj = (6) 



The solution to (6) is 



r 



r re 22Li 





We have specified that this solution is to become 

 negligibly small as the distance from the boundary increases. 

 Thus letting ^-^co , v/e note that it is necessary that C-,2 = 

 C22 = since neither C-i2 nor e^ tends to zero. Hence, for 

 the region near x = 0, we have 



le ^^ le ^ 



^b " '^32^^?'^)® 3 + C^_^2^y,'x)e^ 3 



1/3 ^ 

 or, changing our coordinates back to x by means of x = e ^ , 



