Quasi-orthogonality and differential equations (Q1262987)

The author establishes that quasi-orthogonal polynomials formed from semi-classical or Laguerre-Hahn families of orthogonal polynomials satisfy differential equations of low order (namely two or four). In particular, this applies to linear combinations of orthogonal polynomials for suitable weights. The interest lies in the surprising fact that the order, counter to initial expectation, does not become arbitrarily large.