MULTIPLICATION OF ELLIPTIC FUNCTIONS. ]^<^]^ 



(^n- ^-^) ! 1 ! (^) ! V di' J V -i dj^'J \ Ü d.r'J ' 



accordiiJii' a8 r is even or odd. 

 Siiiiihirly 



+ (-lr.l.8....(2«-t^/--lX%)'-X„_+...+ 1.8. ...C2»,-1)X„| , 

 where A„_,. has the same signification as in (57). 



Let / = 6- = ,^1 -,?)(! -Ä:^^) = ^-(l + ^V+A-V , 



Â- ^ - l-2(l+^•v+3^■v, 



Now write 



(59) -:^D^s = ]^^S,,, 



then by (57) and (5<S) 



((31) S„ = (-1À1.8. ...(2»-2/-3)(2/)%,_,+ ... 



+ i-\y.\.3. ...ßn-'2r--S)(!2/yZ„_,.+ ... + L3. .. (2//.-3)Z„ , 



