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arXiv · 1205.7037

-1 Krall-Jacobi Polynomials

Luc Vinet·Guo-Fu Yu·Alexei Zhedanov
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Abstract

We study a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue equation involving a third order differential operator of Dunkl-type. The orthogonality measure of these polynomials consists in the continuous measure of the little -1 Jacobi polynomials to which is added an arbitrary mass located at the point $x=0$, the middle of the orthogonality interval. This provides the first nontrivial example of Krall-type polynomials with a point mass inside the orthogonality interval. These polynomials can be obtained by a Geronimus transform of the little $q$-Jacobi polynomials in the limit $q=-1$.

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Luc Vinet, Guo-Fu Yu, Alexei Zhedanov. 2015-02-19. -1 Krall-Jacobi Polynomials. https://arxiv.org/abs/1205.7037

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