Researches on the Multiplication 



of Elliptic Functions. 



By 



R. Fujisawa. 



Jacobi, in one of the Suites des notices sur les fonctions eUiptirpies, gives, 

 without cleinonstration, remarkable expressions of sn 2v, sn 3?^, sn 4:V 

 and sn 5u in terms of tlie differential coefficients of \/.r-(l — ,r-xl — A-.r-) 

 and y U~^"X —h-'V-) ^.jj^gj^ y^r[i\^ respect to x\ whereby x stands for 



sn?/.* Namely, writing 



we have 



* Crelle's Journal, Bd. IV, pp. 185-193, and Jacobi's gesammelte Werke, Bd. T, pp. 2G6-275. 



