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Orthogonal polynomials satisfying fourth order differential equations

Published online by Cambridge University Press:  14 November 2011

Allan M. Krall
Allan M. Krall
Affiliation:
McAllister Building, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.
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Synopsis

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.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 271 - 288
Copyright
Copyright © Royal Society of Edinburgh 1981

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