The Szegö curve and Laguerre polynomials with large negative parameters

math.CV

/ Authors

/ Abstract

We study the asymptotic zero distribution of the rescaled Laguerre polynomials, $\displaystyle L_n^{(α_n)}(nz)$, with the parameter $α_n$ varying in such a way that $\displaystyle \lim_{n\rightarrow \infty}α_n/n=-1$. The connection with the so-called Szegö curve will be showed.

The Szegö curve and Laguerre polynomials with large negative parameters

math.CV

/ Authors

Carlos Díaz Mendoza, Ramón Orive

/ Abstract

We study the asymptotic zero distribution of the rescaled Laguerre polynomials, $\displaystyle L_n^{(α_n)}(nz)$, with the parameter $α_n$ varying in such a way that $\displaystyle \lim_{n\rightarrow \infty}α_n/n=-1$. The connection with the so-called Szegö curve will be showed.