Differential orthogonality: Laguerre and Hermite cases with applications Articles uri icon

publication date

  • August 2015

start page

  • 111

end page

  • 130

volume

  • 196

International Standard Serial Number (ISSN)

  • 0021-9045

Electronic International Standard Serial Number (EISSN)

  • 1096-0430

abstract

  • Let mu be a finite positive Borel measure supported on R, L[f] = xf '' + (alpha +1 - x)f' with alpha > -1, or L[f] = 1/2f '' - xf', 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 integral L[Q(n)](x)x(k)d mu(x) = 0 for all 0 <= k <= n - 1. We also provide a fluid dynamics model for the zeros of these polynomials.

keywords

  • orthogonal polynomials; ordinary differential operators; asymptotic analysis; weak star convergence; hydrodynamic