Asymptotics of the Information Entropy for Jacobi and Laguerre Polynomials with Varying Weights Original Research Article

We study the asymptotic behavior as n→∞ of the entropy integral Sn=−∫ p2n, n(x) ln p2n, n(x) wn(x) dx, where pn, n is the nth degree polynomial orthonormal with respect to a Jacobi or Laguerre weight function wn(x) whose parameters grow with n. For this purpose we use the weak-* convergence of the measures p2n, n(x) wn(x) to the Robin distribution of the support of the equilibrium measure in an external field, arising from the limit of the nth root of the sequence of weights.