THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS

Abstract

A new set of orthogonal polynomials is found that are solutions to a sixth order formally self adjoint differential equation. These polynomials are shown to generalize the Legendre and Legendre type polynomials. We also show that these polynomials satisfy many properties shared by the classical orthogonal polynomials of Jacobi, Laguerre and Hermite.