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THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS

Lance L. Littiejohn

Open publisher page 96 citations

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.

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What this paper is about

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.

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OpenAlex reports 96 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Classical orthogonal polynomials, Mathematics, Orthogonal polynomials, Discrete orthogonal polynomials, Laguerre polynomials, Wilson polynomials, Jacobi polynomials, Gegenbauer polynomials

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