MULTIPLICATION OF ELLIPTIC FUN'CTIONS. 



165 



H=0 



1 



1 



,»»+2 



i 



i\ \-z '8! V-z 



1 



3 



-l^ o, J. t ' 





I 





(ni+\)\ '(w + i) 



('Jy;^)! 



-D'" 



or 



(1=0 



m{m~\> 



[2'A.) 2 ^A. = (-l) 2 (-l)"'+V2m.)!l(I~,if" 



1 



1+1 



_1_ ,^ 

 •2\ 1-; 



D'^ 



8! 1- 

 1 jj. s 



3\ i-z' 4! i-z 



1 ^i;.+i ^^' 



[111+ [y. v~z 



{in + n \ 



^ -n-^-M •'^ 



1 s 



1 ^..- ^ 



(w+1)! i-,^ ' (;yi4-'2)! i-^ ' " (2/;^)! l-z 



DeuDtiiig the deteriiiiuaiit on tlie rightbaud side of (--.) by Mo 



and renieinI)ei'iiJi'- 



\ve get l)y division 



P™+i '"^ '' iVf 



iSiibsLitiitiijg this in the .-second of equations (.S.). we (obtain 



