Differential orthogonality: Laguerre and Hermite cases with applications
Abstract
Let μ be a finite positive Borel measure supported on R, [f] =xf''+(α+1-x)f' with α>-1, or [f] =12f''-xf', and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials \Qn\n>m orthogonal with respect to the operator . We also provide a fluid dynamics model for the zeros of these polynomials.
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