ÖFVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1901, N:0 9. 693 



According to (28) we have 



lim ^-^ = M' , 



where M has a signification analogous to that of M . 



If the convergents (4) and (29) are taken accurate enough, 

 ö will be situated between dy and &\ and hence 



lim - = lim M --■= lim M' = G . 

 t 



Therefrom Ave draw the consequence that 6 for all t can be 

 expressed in the form 



e = Gt (30) 



+ one between fixed limits oscillating function. 



Also it foUows immediately from the preceding that G is 

 confined between g^ and g,i as limits. 



Herewith loe have decided a qicestion, ahout lohich, in its 

 general form. hitherto uncertainty has prevailed. 



Owing to the periodicity of the series in the right member 

 of (27) we get 



^ _ ^i(^ + 'Ircml) - 6,{t) 



27tml 



where I denotes some positive or negative integer and dy(t) is 

 identical with 6^. 



Assuming w = 2 in (1) we get 



j,giß ^ A^e'^^^ + A^/3^-* , 



and thus according as we admit the condition (24), (25) or (26) 

 we immediately receive by passing to the limit in (24'), (25') 

 or (26') 



G = g,, G^ g._ or G - ^^^. (32) 



When the modulus of one of the coefficients A, say Aq, is 

 greater than the sum of the remaining A^ it is easy to deter- 

 mine G. 



