?)14 



H. NAGAÜKA. 



where 



/^i, u., (]cuo\\u<j^ the limits of intei^Tntion witli resper-t to //. 



Ev:iln:iiiii£;' tliese two iiidetenniiiatc forin.-; K' •nul L', we find 



K 



2 ;- n. + sin (2 ;- ii) 



L' = 



sin y (?fi + 71.,) sin y {il., — iii) 



Thn.-! tlu' expressions nhove deduced cnn 1)e employed fnv cnleulnting' 

 A' ;iiid L ïifV nil values of ç. 



I may here remark, tliouo-h it has nothing' to dn with theqnestion 

 of ditfra''tion, that a m<^re gvneral integ'ral of the firm 



/'', i ? ens (f . 2 V 

 d(f e ^ sui (f, 



the limits lying' between - and —z can he made to depend on ./"(nr), 

 hy exactly the same process as al)ove given. Tn fu-t, r^essefs function 

 of tlie first kind with index v can he expressed hy means of the 

 f )llowing f )rmula, 



J\.2.ö...{-2v-l) yi? sinç 2çsinç^ n + l J^jn::) \ 



