Oscillatinor Dirich let's Integrals. 



51 



and 



^« = -""-"1^) 



since 



ß(a) r^ e{cd) ^ 6>(^), 



Hence we have 



K«)--f±ic'-"rW = A-/J 



(ß) 



Therefore 



K^^^^ Vl2a^m<l 



since ^s/o" -K^a'. Thus we obtain 



as i^->x . 



Next consider the case in which 



h = Ç>, a = 0. 



Then we have 



f p = ß(x), a'= - X-' e,(x), 



\ e < ^e„ a, > i. 



In this case 



6 a'r 



x(Ä-ff') l-a' ' 



Hence 



r = — -^, ocf<r> (T"(^—x'^a'. 



' -' a' — '— -<^ a 



aY + a"r 



