Asymptotic representation of Stirling numbers of the second kind
By: by W.E. Bleick and Peter C.C. Wang
Contributors: Wang, Peter C.C., 1937-; Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1977
Place of publication: Monterey, California
Language: eng
Number of pages: 10
Subjects: Approximation theory; Combinatorial analysis; Asymptotic expansions
Description: 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.
Notes: 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)

"Approved for public release; distribution unlimited"--Cover.

Technical report; 1977.

kmc/kmc 9/9/09.