Geodesic
Burchnall--Chaundy Polynomials and Dunkl--Darboux Operators
Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 284-291.

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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. 
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     title = {Burchnall--Chaundy {Polynomials} and {Dunkl--Darboux} {Operators}},
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V. V. Meshcheryakov. Burchnall--Chaundy Polynomials and Dunkl--Darboux Operators. Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 284-291. http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a9/

[1] C. F. Dunkl, “Differential-difference operators associated to reflection groups”, Trans. Amer. Math. Soc., 311:1 (1989), 167–183 | DOI | MR | Zbl

[2] Yu. Yu. Berest, A. P. Veselov, “Printsip Gyuigensa i integriruemost”, UMN, 49:6 (300) (1994), 7–78 | MR | Zbl

[3] S. P. Khekalo, V. V. Mescheryakov, “Semeistvo sobstvennykh funktsii operatorov Darbu–Dunkla”, Mezhdunarodnaya konferentsiya po differentsialnym uravneniyam i dinamicheskim sistemam (Suzdal, 2012), MIAN, M., 2012, 175–177

[4] S. P. Khekalo, Differentsialno-raznostnye analogi operatorov Dunkla na pryamoi, assotsiirovannye s mnogochlenami Burchnalla–Chaundi, Preprint 01/2013, POMI RAN, SPb., 2013

[5] J. L. Burchnall, T. W. Chaundy, “A set of differential equations which can be solved by polynomials”, Proc. London Math. Soc. (2), 30:1 (1929–30), 401–414 | MR | Zbl

[6] Y. Berest, “Hierarchies of Huygens' operators and Hadamard's conjecture”, Acta Appl. Math., 53:2 (1998), 125–185 | DOI | MR | Zbl