eg Art. 4. — M. Kuniyeda : 



Since a < nb, Theorem VI may he applied to the integral S„(^), 

 and we ohtain 



Since fj > pi> ■•• > fn-i, we have 



CiW > a(/l) > ••• > C',.(/), 

 and hence we ohtain 



Thus, in the case b > 0, always we have 



Thus the proof is completed for the case b > 0. 

 39- Next we consider the case in which 



= 0. 



Thus a'=-x''H,, ('A>1, 



p = x'" 0. 

 We observe that, if a = 1, 6» < Ö^ ; 

 ifa = 0, 6/>0i. 



In this case xa' = — 0i. 



(i) If a > 0, we have 



n 



xa 



T + —V ^7^^ <^ — « a; 



Kf ^ ^'^ W 



and, for any positive integer n, 



Hence, if a>0, then the method of the last paragraph fails, 

 (ii) Now consider the case in which 



a = 0. 



