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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.

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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