Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Orthogonal polynomials satisfying fourth order differential equations

Allan M. Kralla1

a1 McAllister Building, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.


These polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends. Each set satisfies a fourth order differential equation of the form Ly = λny, where the coefficients of the operator L depends only upon the independent variable. The polynomials also have other properties, which are usually associated with the classical orthogonal polynomials.

(Received October 29 1979)

(Revised April 22 1980)


† Supported in part by U.S. Air Force Grant AFOSR-78-3508.