MULTIPLICATION OF ELLIPTIC FUNCTIONS. ^99 



D,„ik) = Ä""A.(y ), DIM = ^-.«(y )• 



Observe that A.2,„, i>2,„, C'o,„, 1A,,„, Jl,,,, 1>2„„ C'l„„ 1>2,„ are integral functions 

 of ¥ of the degree at niost equal to vi. 



§ 15. 



Consider iirät the case where n is an odd number, and put 

 n2__ 1 = 4^^ sq. 



Introducing the new variable ç = ^/W x in 



Sn 7/7/ = 





we get 



(107) -y/k snna - 



where «am? ^^2m '^I'e rational integral functions of « = ^ • + — . 



We may suppose A and i> to be arranged according to the 

 powers of a, thus : — 



A ^ lA„,x"'^ - ycuj''" ^ ^E,jjy\ 

 (108) 



