Asymptotics of the information entropy for Jacobi and Laguerre polynomialswith varying weights

Citation
Vs. Buyarov et al., Asymptotics of the information entropy for Jacobi and Laguerre polynomialswith varying weights, J APPROX TH, 99(1), 1999, pp. 153-166
Citations number
24
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
99
Issue
1
Year of publication
1999
Pages
153 - 166
Database
ISI
SICI code
0021-9045(199907)99:1<153:AOTIEF>2.0.ZU;2-L
Abstract
We study the asymptotic behavior as n --> infinity of the entropy integral S-n = - integral p(n, n)(2)(x) ln p(n, n)(2)(x) w(n)(x) dx, where p(n, n) i s the nth degree polynomial orthonormal with respect to a Jacobi or Laguerr e weight function w(n)(x) whose parameters grow with n. For this purpose we use the weak-* convergence of the measures p(n, n)(2)(x)w(n)(x) to the Rob in distribution of the support of the equilibrium measure in an external fi eld, arising from the limit of the nth root of the sequence of weights. (C) 1999 Academic Press.