Oscillating Dirichlet's Integrals. 3]^ 



SO that we have 



whence it follows that, for sufficiently large fixed values of z'., the 

 equation (30) has one, and only one, root o.. Thus the function 

 <p has one stationary value. 

 By (30), we have 



SO that (f (a) tends to zero as >^.->co . 



(ii) Let p = Ax{\—]> x)], 



where ^ > 0, p>Ç>, p< 1. 



Then f = ^^^^'') 



and -^ = gives 



If we write 



?. + <7' 



7 



p = a y, 



so that r <0» (^'r < 1, 



then we have 



