MULTIPLICATION OF ELLIPTIC FUNCTIONS. 



173 



vvliere 



(45.; iVi = 



a! 

 J_ 



4! 



D's, 



_1_ 

 4! 



1 



D% 



■•■(w+i)! 

 5! ' ■••(m + '2)! 





[m+lû '(m + 2)! '"•('Jw-ljr 



(46.) iV. 



'-fl ■' 



1 



Z)2 



1! 41-.:;)' '2! ;2a-^)' 



——D''"' — - 



ml z[i-~z) 



i.ß. •' 



'-D^ •' 



1 



D 



m+l 



2! nl--^)' 'àl -ni-'?)' ■■■(w+1)! ^1-^) 



l.Z)- ' 



A _2)™+^ - 



J)2n 



ml z{i - z)' [m + 1 )! z{l-zy '" C2m - 1)! z{ i-z) 



(47.) N, = 



1 



D 



1 .Z)._ '^ 



^D" 



1 !^( 1 - A:-'^)' 2 ! ,^( 1 - Ä2?)' ■ • • m\ z{l- Pz) 



\d^. ' 



1 



■D 



1 



D" 



2 ! ^(1 - A-2^)' -öl z{\- k-z)' ■ • • {m+ 1)! ^(1 - A-2 



i.D- ' 



1 s 



1 



D- 



»il z{l-k'z)' {i)i+\y z{i-k'zy " (2';/i-Jj! z{l-k^z) 



(4S.) iV 



1 2)^ J-D^^ 



1 ! 



^ I z 



2 ! 



3! z 



nil z 



^ Jjm + l '*'' 



(m+l)! ^ 



-^D" 



^ £)m + l "^ 



i^ J)2fft-1 ^ 



(m+ly! - ' '" i'^m-^y z 



It will be observed that the loriuulie of ^wnn for // = 2, o, 4, 5, 

 are those given by Jacobi in the Memoir referred to, which appeared 



