Differential orthogonality: Laguerre and Hermite cases with applications

Let $\mu$ be a finite positive Borel measure supported on R, $\LL[f] =xf’‘+(\alpha+1-x)f’$with$\alpha>-1$,or$\LL[f] =\frac{1}{2}f’‘-xf’$,and$m$ a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials $\{Q_n{\}}_{n>m}$ orthogonal with respect to the operator $\text{LL}$. We also provide a fluid dynamics model for the zeros of these polynomials.