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The Heun operator of Hahn type

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arxiv 1808.00153 v1 pith:EDV44RHO submitted 2018-07-17 math.CA math-phmath.MP

Luc Vinet , Alexei Zhedanov This is my paper · ORCID
classification math.CAmath-phmath.MP
keywords operatorhahnpolynomialsalgebradegreeheun-hahnuniformbases
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abstract

The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree $n$ to polynomials of degree $n+1$, to be tridiagonal in bases made out of either Pochhammer or Hahn polynomials and to be bilinear in the operators of the Hahn algebra. The extension of this algebra that includes the Heun-Hahn operator as generator is described. Biorthogonal rational functions on uniform grids are shown to be related to this framework.

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  1. The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra

    math-ph 2026-05 unverdicted novelty 5.0 of 10

    The symmetry algebra of the Smorodinsky-Winternitz II system is identified as the Laguerre-Heun algebra through explicit operators Y, W and their commutation relations.

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