The Dubov-Eleonskii-Kulagin polynomials and a modification of the Christoffel formula

6 Oct 2021  ·  Rachel Bailey, Maxim Derevyagin ·

In this note we demonstrate that the polynomials introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra are a discrete Darboux transformation of Hermite polynomials. In particular, we obtain a modification of the Christoffel formula since its classical form cannot be applied in this case...

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Mathematical Physics Classical Analysis and ODEs Mathematical Physics Primary 33C45, 42C05, Secondary 47B36, 15A23