Integral estimates for Laguerre polynomials with exponential weight function (Q2191889)

This paper deals with the system of functions \(\{\lambda_n\}_{n\in\mathbb N}\) orthogonal with respect to the Sobolev-type inner product \[ \langle f,g \rangle= f(0) g(0)+\int_{0}^\infty f'(x) g'(x) dx. \] These functions are expressed in terms of classical Laguerre polynomials and using several of their properties some asymptotic formulas for the functions \(\lambda_n(x)\) on \([0,\infty)\) with \(n\to \infty\) are derived.