Asymptotic Representation of Stirling Numbers of the Second Kind.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 09, 1977
- Accession Number
- ADA035713
Entities
People
- Peter C. C. Wang
- W. E. Bleick
Organizations
- Naval Postgraduate School