Oscillating Dirichlefs Integrals. 



if Or^ A, %1 ^ 1 . 



0(0) 



8(a) ^ • 

 Hence it follows that in all cases we liave 



Thus we obtain ^(«) ^ ^,cß^ 



as -^->oo , 



31. (ii) Let a= -1 and & > 1. 

 In this case we have 



53 



^^"^-^=^ gi^-e^^ 



/ — <t' 





&' 



Now -^^(l + è).._|^_^,, 



since > ^»6»'. Hence the equation for x = a takes the form 



-a'(œ)t(œ) = ;., 

 where ^-^ - (l + ô)-|^ > l. Hence we have 



>^ " t(a) 



whence 



<1, 





'{a) 



an<^l a>d 



by Lemma 5. 



Now é(d) = i^(^) - ^K&) 



