Burchnall–Chaundy Polynomials and Dunkl–Darboux Operators

V. V. Meshcheryakov

State Socio-Humanitarian University, Kolomna, Moscow region

Abstract: Certain properties of Burchnall–Chaundy polynomials are studied. The first two nonzero coefficients following the leading coefficient are calculated in explicit form. The Dunkl–Darboux differential-difference operators related to the Burchnall–Chaundy polynomials are considered. The eigenfunctions of these operators are described.

Keywords: Burchnall–Chaundy polynomial, Bessel function, Dunkl–Darboux operator.

UDC: 517

Received: 01.06.2015
Revised: 16.09.2016

DOI: 10.4213/mzm10803

 English version: Mathematical Notes, 2017, 102:2, 261–267

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