Asymptotic Representation of Stirling Numbers of the Second Kind
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Authors
Bleick, Willard Evan
Wang, Peter C.C.
Subjects
Asymptotic representation
Stirling numbers of the second kind
Bell number
Hermite's formula for a divided difference
Stirling numbers of the second kind
Bell number
Hermite's formula for a divided difference
Advisors
Date of Issue
1977-02-09
Date
2/9/1977
Publisher
Monterey, California. Naval Postgraduate School
Language
eng
Abstract
The distribution of the Stirling numbers S(n,k) of the second kind with respect to k has been shown to be asymptotically normal near the mode. A new single-term asymptotic representation of S(n,k), more effective for large k, is given here. It is based on Hermite's formula for a divided difference and the use of sectional areas normal to the body diagonal of a unit hypercube in k-space. A proof is given that the distribution of these areas is asymptotically normal. A numerical comparison is made with the Harper representation for n=200
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-53BL77021
Sponsors
Office of Naval Research (Dr. Bruce McDonald), Statistics and Probability Branch, Arlington, VA
Funder
NR-042-286, NSWSES-56953, NISC-56969
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.