MULTIPLICATION OF ELLIPTIC FUNCTIONS. 



187 



Thus we find C = (-1)'" and thence 



Çrl) 



^^'''' ■■■i^irf 



{»i + 1 



,D"'^\9, 



(2«i)! 



D-'^s 



/ 1 \m^,'2iii + l 



1 ^d1 



s ' lis 



lis' 2 ! s 



^ — _D"'+i2 



■■■ {m+l)\ s 





which identity may nhso be proved directly in the manner exempli hed 

 by the particular case m =^^2. 



§ 11- 



Consider next the case // even. Referring' to § 6, if we take 

 \-Q instead of i'+C^As, we sh-all have in place of (oO) the following 



determinant 



