Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

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2014-05-01

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Elsevier B.V.

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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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Journal Of Approximation Theory. San Diego: Academic Press Inc Elsevier Science, v. 181, p. 18-29, 2014.

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