Publication: Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials
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Undergraduate course
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Elsevier B.V.
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Article
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Abstract
Denote by (P) over cap ((alpha,beta))(n) (x) the X-1-Jacobi polynomial of degree n. These polynomials were introduced and studied recently by Gomez-Ullate, Kamran and Milson in a series of papers. In this note we establish some properties of the zeros of (P) over cap ((alpha,beta))(n) (x), such as interlacing and monotonicity with respect to the parameters a and beta. They turn out to possess an electrostatic interpretation. The vector, whose components are the zeros, is a saddle point of the energy of the corresponding logarithmic field. (c) 2014 Elsevier Inc. All rights reserved.
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X-1 Jacobi polynomials, Orthogonal polynomials, Zeros, Electrostatic interpretation
Language
English
Citation
Journal Of Approximation Theory. San Diego: Academic Press Inc Elsevier Science, v. 181, p. 18-29, 2014.
