ÖEVEESIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1901, N:0 9. 699 



and hence by (49) 



Q^9jL±li^ (50) 



agreeing with the last result in (32). 



If we have several polynomials such as 



;=1 

 n 



r = l 

 n 



and the relation 



F{f) = F,{i)F^{t) . . . Flt) 



holds, and M^, M^, . . ., Ms have the same significations in 

 respect to F.^{t), F^{t), . . ., Fs{t) as IT has relating to F{t), 

 then it follows ininiediately from the preceding that the relation 



M=^ M^ + M, + ... + Ms (51) 



also holds. 



Now the results in (24') and (25') follow from (35) and the 

 result in (26') from (48) with the aid of the two former results. 

 Thus upon the whole the propositions in (24'), (25') and (26') 

 are derivable without the assistance of the formula (21). 



From this reason it is possible to determine M in (21') 

 independent of (21). 



Indeed, the M corresponding to the elementary factor 



1 '■r 1 '■r O 



i — t i — i — t i — i — t 



g m o m -— o m g m „ m 



in (12), according to (24'), (25') and (26'), has the values — , 



O, ^7— according as 

 2m 



.2, 



i — 



e ™ 



is less, greater or equal to unity. 



