Weak asymptotics for the generating polynomials of the stirling numbers ofthe second kind

Authors
Elbert, C
Citation
C. Elbert, Weak asymptotics for the generating polynomials of the stirling numbers ofthe second kind, J APPROX TH, 109(2), 2001, pp. 218-228
Citations number
11
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
109
Issue
2
Year of publication
2001
Pages
218 - 228
Database
ISI
SICI code
0021-9045(200104)109:2<218:WAFTGP>2.0.ZU;2-0
Abstract
For the horizontal generating functions P-n(z)=Sigma (n)(k=1) S(n, k)z(k) o f the Stirling numbers of the second kind, a weak asymptotic is established , as n -->x. The distribution function F-n of the zeros of Q(n)(z)= P-n(nz) is investigated and by using the Stieltjes transformation. the limit of F- n in the sense of weak convergence is deduced. (C) 2001 Academic Press.