702 CA VALLIN, SECÜLAR PERTÜRBATIONS. 



In fact, by (12) 



2 a. 



i — t 



.a'e ™ 



r = \ 



""'tl U\ 



and hence 



,—c l i- i — \ 



?■ = ! 



i « »re,. 



i — t 



= 1 



= a!" TT \«^* — e"'}, 



a polynomial of the degree jUj in respect to az^. 

 The coefficients in the polynomial 



Prl- i'^\ 



TT \ «^^' —e""} 



r = l 



can by the aid of the fonnulas of Neayton be expressed in func- 

 tion of the sum of powers of the roots of the original equation 

 (10) and the latter in their order by means of the formula of 

 Waring directly in function of the coefficients of the same 

 equation. 



In this manner we obtain according to (56) a convergent 

 to M{a), in which after the operations are performed we may 

 put t = 0, the more accurate the greater k is. 



Next we will deduce a relation between M{a) and known 

 functions. 



To this purpose we commence by deducing sorae general 

 propositions. 



Asume 



00 



