DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 351 



I. Rr t > Rr K 



(27) 4**.** = **"'% CUx... 



ttlJ x 



c 



XX . . 



- X d *j*~ {r *- TK) 2 2 tZ+^vAiogx^dx, 



c c i=1 J- 1 



t integrations 



where h t j is a positive integer whose value it will Dot be necessary to 

 write out, noting, however, that: 



(28) h u <e K -X. 



II. Rr k = Rr K . 



a) k -^ k. I < L . 



(W) # ***r* = « rrt 2 fcdx... 



fc=l J X 



o 



x x 







t integrations 



. . J±dzJz-< r '-*J 2 2 ^^.^/..Oog^tfe. 



5) *:{:*, L<l<e k . 



X XX 



(30) *— ■ s£f*[/> • • ■/=*/= B ~^ J *«•" * 



(log x) 



c c c 



(£ — Z) integrations 



t-l-L x XX 



+ 2 J - ** • • J - J* J *~ {n) 2 2 ^ *w . G<* «)*" ^ 



c c c *— - 1 J= 



£ integrations 



e) k = K, I < A. 



(31) <k,/, f+ i = 2 I x^ '" 



o 



* i f* * =m 3— e i 









< integrations , 



