The monic Laguerre polynomials preserve real-rootedness

Praveen S. Venkataramana

Let $L_n(x)$ and $L_n^{\alpha }(x)$ be the $n$th Laguerre and associated Laguerre polynomial respectively. Fisk proved that the linear operator sending $x^n$ to $L_n(x)$ preserves real-roo…