MULTIPLICATION OF ELLIPTIC FUNCTIONS. 



171 



Writing-, as is usutil, 



S. 8. 





so that 



^/z = so?« , 



we have, in virtue of equiition« (3.) and (2(S.), 



V'c — — sn mi, 



vr 



= cunu, 



where n is any even or odd integer. 



When // is odd, say // = 2m + 1, we have from (16.), (19.), (-o.) 

 and (27.) 



I sn nu = { — \)^z 



M ' 



(89.) 



en nu — (1 — ^)- 



^ ilf. 



M ' 





where 



(40.) ilA 



M ' 



1 ,s 1 .<? 



'2! 2 ' 3! ^ ' 



1 .s 



4d'- 



1-D'-' 



1 ,9 



8! ^ ' 4! ;? ' ■•■(m+'2)! ^ 



1 .s 



1 sis 



^ T)TO+2 ^ ^ r)2?» 



(w+1)! ,r ' (7» + '2)! ^ '■■' i2w)! 



