Some properties of orthogonal polynomials for Laguerre-type weights (Q535512)

Let \(R: \mathbb{R}^+ \rightarrow \mathbb{R}^+\) be a continuous, nonnegative, and increasing function, and let \(p_{n,\rho}(x)\) be the orthonormal polynomials with the weight \(w_\rho(x)=x^\rho e^{-R(x)}\), \(\rho>-1/2\). The authors give estimates for the higher-order derivatives of \(p_{n,\rho}(x)\) at their zeros and establish asymptotic expansions for various weighted \(L_p\)-norms, \(0<p\leq \infty\). These estimations are important to clarify convergence issues for the higher-order Hermite-Fejér interpolation polynomials.