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The dominant integral. We now evaluate the integral in the above expression. For convenience, wewrite e '.x/=2 D e u.x/=2 .1 C ! 2 .x/=/, whereu.x/ D x 2 log.1 /and ! 2 .x/ D C 1 x C C 2 x 3 :Obviously, u. x/ D u.x/ and ! 2 . x/ D ! 2 .x/. Thus, for x satisfying ju.x/j 1=2 ,!!2ˇh.x/ C h. x/ D ‰.x/˛ˇe u.x/=2 ˇ1ˇ˛2 C O j˛ 1j! 2 .x/ˇ.e u.x/=2 1/ ˇ C 1 C x6:Consequently,Z 1=10Zh.t/ dt D 1=10ZD 2D.h.t/ C h. t// dt C O0
Page 1 and 2: Uniform asymptotics of Poisson appr
Page 3 and 4: Note that if p > 1=2, we can interc
Page 5 and 6: On the other hand, another natural
Page 7 and 8: To prove Theorem 2.1, let ı n;m WD
Page 9 and 10: Proof. The upper bound of (2.7) fol
Page 11 and 12: 2.5 The usual LLT for S nWith the a
Page 13 and 14: It follows thatE.t/ C 22 .eit 1/ 2
Page 15 and 16: Proposition 2.10. Assume K > 0 an
Page 17 and 18: Note that by (2.35) the terms insid
Page 19 and 20: for sufficiently small , where c 4
Page 21 and 22: we can apply the same proof used fo
Page 23: uniformly for x bounded away from t
Page 27 and 28: [5] A. D. BARBOUR, L. HOLST AND S.

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