Differential orthogonality: Laguerre and Hermite cases with applications.

Let μ be a finite positive Borel measure supported on R , L [ f ] = x f ″ + ( α + 1 − x ) f ′ with α > − 1 , or L [ f ] = 1 2 f ″ − x f ′ , and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials { Q n } n > m that satisfy the orthogonality relations ∫ L [ Q n ] ( x ) x k d μ ( x ) = 0 for all 0 ≤ k ≤ n − 1 . We also provide a fluid dynamics model for the zeros of these polynomials. [ABSTRACT FROM AUTHOR]