Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure

Abstract

This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure: \[ \frac{1}{x-c}x^{α}e^{-x}dx+Nδ(x-c), \] for $x\in [0,\infty )$, $\alpha >-1$, a free parameter $N\in {\mathbb{R}}_{+}$ and a shift $c<0$. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as $n$ tends to infinity.

17 pages, no figures