Asymptotics of the Best Constant in a Certain Markov-Type Inequality Original Research Article

Let ‖·‖ be the weighted L2-norm with Laguerre weight w(t)=tαe−t, α>−1. Let Pn be the set of all complex polynomials whose degree does not exceed n, and γn(α)≔supp∈Pn(‖p′‖/‖p‖). We show that γn(α)/n→(j(α−1)/2, 1)−1 as n→∞, where jν, 1 is the first positive zero of the Bessel function Jν(z).