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Differential orthogonality: Laguerre and Hermite cases with applications. (English) Zbl 1321.33011

The authors consider orthogonal polynomials with respect to a Laguerre or Hermite differential operator and a positive Borel measure with unbounded support on \(R\). They study some analytic, algebraic and asymptotic properties of the sequence of orthogonal polynomials with respect of the above operators. They also give some results concerning the zeros of the polynomials. Finally they show a hydrodynamic model for the zeros of these orthogonal polynomials.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
47E05 General theory of ordinary differential operators
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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