70 Art. 4.— M. Kuniyecla: 



Then in the integral 



./ ax \ x(7 j 

 we have _/^ _ _ _^ v. i 



Let UP write 



Six, 1) ^ _ d f 6 \ 



Ô»! "^ dx\ äj' 



SO that ^ (^' 1) = ^ {-^ - -^} < ^ 



since x6' < S and xO^' < 6*1. We observe that, since -s- > !■ we 

 have Ö(a?, 1) > 0, and 6{x, 1) is a function of t]ie same type as 0, 

 namely 



x^ < 8(x, 1) < {l/xf. 



Thus we have 



./ .X 



wJiere ,oi = — ^ ' ^ • 



If 0(a;, 1) < (9j, then /^i < xa' and, as before, applying Theorem 

 VI, Ave see tliat 



If 6(x, 1) <-j A6i-, then, by proceeding as in the case 6 f^ AS^, we 

 easily arrive at the same result. 



If 6{x, 1) > &i-, tlien repeat a similar process. 



Thus we have to consider successively the functions 0(x, 1), 

 6{x,2,), , 6{x,n) defined l)y the equations 



