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Addition Formula and Related Integral Equations for Heine–Stieltjes Polynomials

Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P. O. Box 413, Milwaukee, WI 53201, USA
Symmetry 2019, 11(10), 1231; https://doi.org/10.3390/sym11101231
Received: 4 August 2019 / Revised: 23 September 2019 / Accepted: 26 September 2019 / Published: 2 October 2019
(This article belongs to the Special Issue Symmetry in Special Functions and Orthogonal Polynomials)
It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found. View Full-Text
Keywords: Heine–Stieltjes polynomials; spherical harmonics; reproducing kernel; Dunkl equation Heine–Stieltjes polynomials; spherical harmonics; reproducing kernel; Dunkl equation
MDPI and ACS Style

Volkmer, H. Addition Formula and Related Integral Equations for Heine–Stieltjes Polynomials. Symmetry 2019, 11, 1231.

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