Wang 



N 

 H(T) = iT-'(T^-l)-"'^{r' dh^pM,^^ ^ ^ b„T"} . (42) 



'' n = 



However, to satisfy (21), bf, have to be purely real. The condition 

 (33) is equivalent to 



H(t)— as |t| -^ oo, (43) 



since near |z| = oo 



T ~ a^z'/^. (44) 



To satisfy (43) , 



bn = for n> 2. (45) 



Due to the symmetry of our problem, which implies 



Im f = on CI, (46) 



and due to the fact that the differential operator L is purely real on 

 CI, we require that 



bo=0. (47) 



This leaves only the constant b| undetermined. After carrying out 

 the integrations in (42) , we may write 



^^''^ = 2l^7?rF5:rnt J(Ka.)^M,(T) + {K^fuj^r) 



- 2TrjKwT +b|T2(T2-l)'/2] , (48) 



where 



M,(T) = TrTV^-l)(4T+Tr) + t^(t^-I)'''^ [ 2Tr - |- 4(1 +7r)T^] 



- 2t^(t2- 1)3/2 ^ ^ . 2t2(t2-1)'/2>(t) , (49) 



198 



