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Asymptotic representation of Stirling numbers of the second kind

by: Bleick, Willard Evan, 1970-;Wang, Peter C.C., 1937-

Publication date: 1977-02-09

Topics: SYSTEMS ENGINEERING., RELIABILITY (ENGINEERING)--MATHEMATICAL MODELS.

Publisher: Monterey, California : Naval Postgraduate School

Collection: navalpostgraduateschoollibrary; fedlink; americana

Contributor: Naval Postgraduate School, Dudley Knox Library

Language: English

Title from cover

"Prepared for: Office of Naval Research, Statistics and Probability Branch"--Cover

"9 February 1977"--Cover

"NPS-53BL77021"--Cover

DTIC Identifiers: Stirling numbers, Hermite functions, Bell numbers, WUNR042286

Author(s) key words: Asymptotic representation, Stirling numbers of the second kind, Bell number, Hermite's formula for a divided difference

Includes bibliographical references (p. 5)

Technical report; 1977

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

kmc/kmc 9/9/09