MULTIPLICATION OF ELLIPTIC FUNCTIONS. 



191 



forms wliicli ;ire ex]!rf;8.siL)le Ijy 11,,. On introducing B,,, it ^^ï\\ be 

 seen that there comes out ;i certain power of.s- as a factor in the numera- 

 tor as well as in the denominator, which may lie cancelJed ayainst 

 each othei', leaving" rational integral functions of -y/z ^ sn // both in 

 the ntunerator and the denoniiiiator. The final results are: 



11 odd, /// = -— , 



(cS'i) i=,ii lilt =(-l)"'y^^ 



1, ±\--.\-l^z, m-zA-K'zf, ...C2.1-,ï.l-A:2^)"'+' 

 0, 1, B„ ... B,„ 



1, Bi, 



B„ 



B. 



-^^;;t-l> -^^m» 



1 > 



i?o 



(8;i) en na ^\/l —■<^ 



1, -±y.\-1^z, !:l.zl-hrzf, ...(-2.^.1 -Â-?)"'+i 



0, 1, Bi ... B,„ 



1, iv'i. Bo, ... -R,„a 



■^Art-l) J^tio 



B„i+i, 



JrCq,, 



(«4) dn nil == V 1 — A'-^i 



1, -~±A'z.\~z, {-2.Pz.l-zf, ...{-±Ji^:A-zr'' 



0, 1, Bi, ... B„t 



1, il'i, iV.^, ... B„,^y 



B,, 



B,,,, 



B„ 



B., 



(Ö5) 



(küjoni. 



1, By, ...B„, 



B„ Bo, ...B,„+, 



