ABSTRACT

Because l z l s (Rez) csc6 this is O{exp(-kn lzl sin6)) as z -, m in Iphz(g +n-6. Combination of this estimate with (3.05) yields (3.03).

114 4 Contour Integrals

3.4 Theorem 3.3 Assume that: (i) q(t) is holomorphic within the sector S: a, < plit < a,, where a, < 0 and

a, > 0. (ii) For each 6 E (0, $a, -fal) the expansion (3.02) holds as t -+ 0 in the sector Sb: a ,+6 ,<ph t<a2-6 . Again,p>OandReR>O. (iii) q(t) = O(e"lfl) as t -r oo in Sb , where a is an assignable constant.