MULTIPLICATION OF ELLIPTIC FUNCTIONS. 



167 



or 



ti=m+l 

 )i=0 



m(m—l) 



C20.) 2 iV/^-"'+'^''=(-ir^X-l) ' (2m)!!(l-^^Ä')' 



2.A2(n+l 



^^D^^ 



'J! l-A-2^' 



1.^. '^ 



1 



8! i-^'^ 



3! l-A'^' 4! l-A'^^ 



-.D 



TO+1_ 



1 .. 



(;« + 'i)! i — A-^ 



1 



.D 



»i+i. 



-.D" 



1 ,s 



>+T)r 1-^2^ ' (7;i + 2)! 1 - A-2-J ' ■ • ■ {'2m)\ 1 - Ä;^^ 

 Cull the dererininarit on the righthand side of (26.) M„ we liave 



p -(I-A^j -^ . 



SubstitutiDg this in the last of equations (8.) we obtain 



C27.) 



Vi-A'c = (i-^'-2)' 



M ' 



§. (;. 



In case // is even, sny // = 2»?, put m = q - i, and, referring to 

 §. 1., let one of the 2^/ points in which 7^ + Qs vanishes, coincide with 

 the point IC I ^}, another point witli |0 | 0)-, and the remaining 

 (2q-2) ])oints with the point {z \ s\ . Then 



(28.) 



dZ , dz ,, 



—^ + II = , n even, 



s 



and 



P-\-Qs = [a,z + a.j- +...+ <*,„+i^"'+') + {K+byZ+...+ b„,^,z^"^')s, 



