Oscillatino- Dirichlet's Integrals. 23 



and £ = +1 or e = —1 according as --->0 or -v-<0. 



Herein put t = '/d (/>0), 



then (-O"" = e^^^'/-^ r' = e-h^^-^ l-\ 



Therefore 



(23) /'V^^r'-^Aogi-Y'W = r(,-)eèr^^/-'-(log/0^-\l + £) 



where hm e = 0, ]ini s' = 0. 



This formula quite agrees with our i-esult obtained for the case in 

 which 



r = —a, — l<;a<0; s = a + mi, 0<a<;], w^O. 



Tlius our result is verified. 



13. Next consider the case in which 



f r=z—a — hi, — l<a<0, 6^0, 

 [ s = a, 0<;«<1. 



dx 



\ ^^«-l In log (l/.r) COS /a- , 



e ax 



./ \ ' X 



./ \ ' X J X 



