6 Mr Greenhill, Complex Multiplication [Oct. 29, 



where D = (1 + -' II 1 + 



icj { en (2s — 1) o)j ' 

 leading to the differential relation 



c% |(1+ i*Jn) dx 



^(l-S/M+^Vl 1 -^-^?)' 

 For instance, when n = 1, then p = 0, c = 1, and 



cum. 

 en | (1 + i) u = a/(— i) 



_, en ?t 



This can easily be verified ; for if we put 



|(1 + 1) u = w, 



then %=(1— *)v, 



and then the above relation gives 



. 1 — i en 2 i (1 + *) w 



en u — % — —. — 5-f-)- ^— , 



1 + ^cn 2 l(l + t)?^' 



1 — i en 2 w 



or 



en (1 — i) v = i J 



+ 1 en v 

 the well-known relation, leading to 



dy _(l—i)dx 



vci-y) = v(i-^)' 



if a? = cnv, y = cn (1 — i) w. 



Again, when- -^ = a/5, 



2&# = V-5 - 2, 



c = V5 + 2 + 2 v / (\/ 5 + 2 )> 

 . V5+1 , /A/5+1 



V c = S r 



