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Construction of Polynomial Eigenfunctions of a Second-Order Linear Differential Equation

  • ORDINARY DIFFERENTIAL EQUATIONS
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Abstract

A system of third-order recurrence relations for the coefficients of polynomial eigenfunctions (PEFs) of a differential equation is solved. A recurrence relation for three consecutive PEFs and a formula for differentiating PEFs are obtained. We consider differential equations one of which generalizes the Hermite and Laguerre differential equations and the other is a generalization of the Jacobi differential equation. For these equations, we construct functions bringing them to self-adjoint form and find conditions under which these functions become weight functions. Examples are given where the PEFs for nonweight functions do not have real zeros.

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REFERENCES

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Authors and Affiliations

  1. Odesa I.I. Mechnykov National University, Odesa, 65082, Ukraine

    V. E. Kruglov

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  1. V. E. Kruglov
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Correspondence to V. E. Kruglov.

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Translated by V. Potapchouck

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Kruglov, V.E. Construction of Polynomial Eigenfunctions of a Second-Order Linear Differential Equation. Diff Equat 59, 1166–1174 (2023). https://doi.org/10.1134/S0012266123090021

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  • DOI: https://doi.org/10.1134/S0012266123090021

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