Laguerre–Sobolev orthogonal polynomials: asymptotics for coherent pairs of type II Original Research Article

Let Sn be polynomials orthogonal with respect to the inner product( f,g)S=∫0∞fg dμ0+λ∫0∞f′g′ dμ1,where dμ0=xαe−x dx, dμ1=xα+1e−xx−ξ dx+Mδξ with α>−1, ξ⩽0, M⩾0, and λ>0. A strong asymptotic on (0,∞), a Mehler–Heine type formula, a Plancherel–Rotach type exterior asymptotic as well as an upper estimate for Sn are obtained. As a consequence, we give asymptotic results for the zeros and critical points of Sn and the distribution of contracted zeros. Some numerical examples are shown.