Differential orthogonality: Laguerre and Hermite cases with applications

Abstract

Let $\mu$ be a finite positive Borel measure supported on R, $\LL[f] =xf''+(α+1-x)f'$ 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.

arXiv admin note: text overlap with arXiv:1303.2479

References in corpus (1)

• On orthogonal polynomials with respect to a class of differential operators

Cited by in corpus (1)

• On Polar Jacobi Polynomials