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
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.