1883.] of Elliptic Functions. 



Then, if x — en u, y = cn^(l+i \/9) u, 



y=^(-l C ) 



1+ £/( 1+ s)( 1+ I 



where a = en \ (K— K'), /3 = en f (K — iK') ; 



and 1 - y 1 = (1 +ic) {l-x) (l - -YYl - |Y-r- D, 



^-^-yc^K^n 1 ^^ 



i>= (i+?K 



^y/ a; 



where a = en f (if - z'iT), /3 =.cn f (/i — «!&''), 7 = en f(K— iK') ; 

 and so on. 



The superior regularity of the periods of the en function, and 

 of the positions of the critical points of the corresponding in- 

 tegral 



dx 



render the en function preferable to the sn and dn function for 

 employment in the general formulae of transformation and of com- 

 plex multiplication. 



