论文信息 - THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS

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.

Lance L. Littiejohn

[1] S. Bochner,et al. Über Sturm-Liouvillesche Polynomsysteme , 1929 .

[2] Allan M. Krall,et al. Orthogonal polynomials satisfying fourth order differential equations , 1981, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[3] R. H. Cole,et al. Theory of ordinary differential equations , 1970 .

[4] A. Erdélyi,et al. Higher Transcendental Functions , 1954 .

[5] T. Chihara,et al. An Introduction to Orthogonal Polynomials , 1979 .

[6] H. L. Krall,et al. Certain differential equations for Tchebycheff polynomials , 1938 .

[7] Peter Lesky,et al. Die charakterisierung der klassischen orthogonalen polynome durch Sturm-Liouvillesche Differentialgleichungen , 1962 .