Differential orthogonality: Laguerre and Hermite cases with applications

Abstract: 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 $\LL$. We also provide a fluid dynamics model for the zeros of these polynomials.