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arXiv · 1504.03297

Differential orthogonality: Laguerre and Hermite cases with applications

J. Borrego-Morell·H. Pijeira-Cabrera
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Abstract

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

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J. Borrego-Morell, H. Pijeira-Cabrera. 2015-04-13. Differential orthogonality: Laguerre and Hermite cases with applications. https://doi.org/10.1016/j.jat.2015.03.005

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