Wang 



AY ' 



1/2 



de> de 



2 ^rv-'/2 



= T^[l 



d' /d^' 



4 ^/.2 



-le; 



3; - 26C + 3 



(65) 



A straightforward expansion of (62) shows that 

 e = 0(;''^) as ;-0, 



(66) 



and, of course, 



r(e) = 0(1) as ;-l. 



(67) 



Equation (66) indicates that the mapping (62) maps the point I to the 

 point at infinity in the ^ -plane. The flow region ICAI in the ^-plane 

 is shown in Fig. 5. From (65) and (66) we can see that 



r(e) = 0(4-) as III -00. 



(68) 



Olver [ 1954] has investigated an equation of the form 



d^ 



de' 



= [Ht'^e +r(e)]u. 



(69) 



where p. is a positive large parameter. He shows that for a domain 

 D, if x{%) is regular in D and r^) = 0( | ^ 1''^^''^) for some o" > 



^- plane 



Fig. 5 A conformal mapping plane of the basic flow 

 region bounded between ICAI 



202 



