DIFFERENTIAL-EQVATIONERS INTEGRERING. 15 



l:o. Hvad P angar, 8a fbljer af den redan i Lemma 1 anfbrda satsen ur JACOBI'S 



afhandlmg "De Determmantibus functionalibus" (Crelles Journ. Tom. 22, pag. 340, Propos. 



*!/ IT>L 



dx ' dxi dx n 



P = rr-r ~~ """i * 



")w n+i dw n+ i 3M> n +i 



dx dxi dx n 



2:o. Hvad vidare U n och Z7 n+1 betraffar, anmarka vi forst, att genom partiell dif- 

 f'erentiering af (19) i afseende pa <f erhalles 



dx-i d(f k dx r dy> k dx n d(p k 



dxi d<p k dx r d(f k dx r d(f k 



hvadan 



vyi v^i v<f\ <^y^i 



dx r _i ' dx r+1 dx n 



dxi dx r _i ' dx r+l dx n 



*_ (p n ,, 



dx! dx r -i ' dx r+1 dx n 



