24 



Art. 4. — M. Kuuivetlii 



Applying Theorems 111 and IV, we can easily see that 



j-i(/) = r(-rt— 6i)f-è(«+*')7i£/»'i'(iog;)«-i(i+£) 



when 



liin £ = 0. 



The integral J-i'^-) may he written in tlie form 

 j^(;.) =|^V«-" (1 -.;— (log ^)--'/'-'»4'"i-"3rf,. 



If we make use of the equations 





g/.nog[i/(i-')] ^ l + 0(rr), 



x"'^ cos >?.a; (^^ = l\(i)A"' cos ^a- 



/■CO 



/ x"'^ sill >^.a; (7a: = Fi^a)/."- 

 wo 



(0<a<l), 



sin iy a - 



\NQ can easily prove that 



=: /'(,S')/.-V(^-^--)»(l+6'), 



where lim ^' = 0- 



Thus we ohtaiii 



/(/) =/,(/) + /,(/) = /|;.)a^.,/-'-(loa;,)-i(i+e) 



where 



lim e = 0, lim e' = 0. 



/ > X /^ X 



Here again we have ohtained the result which quite agrees 

 with the formula (23) fur /,..<(//). 



