Appendix to Quicksort Asymptotics

This appendix to [2] contains a proof of the improved estimates in Remark 7.3 of that paper for the moment generating function of the (normalized) number of comparisons in Quicksort. AMS 2000 subject classifications. Primary 68W40; secondary 68P10, 60F05, 60E10. Date. May 22, 2001. Research supported by NSF grant DMS–9803780, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement of Research in Statistics. 1 This is an appendix to [2], to which we refer for background and notation. The theorem, lemmas, and equations in this appendix are labelled by A.1, etc.; labels with pure numbers refer to [2]. The purpose of this appendix is to provide a proof of the following estimates stated in Remark 7.3 of [2]. Theorem A.1. Let L0 . = 5.018 be the largest root of e = 6L2. Then, for all n ≥ 0,