MULTIPLTOATTOX OF ELLIPTIC FUXCTTOXS. 



1()1) 



(31.) {Pi+p,:+ ..■\-p„„,:"'\ + ia+^w+ •. + a.-ir'n = o- 



Hence 



Herein putting Z=0, Z = l, Z = -7;2 successively, we oLtnin, after sligh) 

 reduction, 



(88.) ^ ^Yzr^d^zY ^ 



Vi-A'r(i-/.-.?y" = 



^ m+1 



PiA-"' + PoA-"'"^+... + P„Hi 



Tlie reduction of (he expressions ■which occur on the rig'hthand 

 side of (38.) runs on the r;anie line as tlie reduction of the corresponding 

 expressions when n is odd, discnssed somewhat in detail in preceding 

 sections. We niay therefore at once w'rite down tlie results ; 



(34.) 



i'„Hi = (-l) ' C27;i-1,!: 



\\^ z 



2! 



in\ z 



8! ;? ' •••(w+])!^ z 



m\ z '(m+1)! z ' '■- {2m-\)\ 



B"- 



