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Orthogonal Polynomials With Weight Function (1 - x)α( l + x)β + Mδ(x + 1) + Nδ(x - 1)

Published online by Cambridge University Press:  20 November 2018

Tom H. Koornwinder
Tom H. Koornwinder*
Affiliation:
Mathemattsch CentrumP.O. Box 4079, 1009 AB Amsterdam, Netherlands
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Abstract

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We study orthogonal polynomials for which the weight function is a linear combination of the Jacobi weight function and two delta functions at 1 and — 1. These polynomials can be expressed as 4F3 hypergeometric functions and they satisfy second order differential equations. They include Krall’s Jacobi type polynomials as special cases. The fourth order differential equation for the latter polynomials is derived in a more simple way.

Keywords

33A6533A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 205 - 214
Copyright
Copyright © Canadian Mathematical Society 1984

References

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