Higher-order differential equations with polynomial solutions associated with classical orthogonal polynomials

1Makarov, VL
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 7:3-9
Section: Mathematics
Language: Ukrainian

A constructive algorithm for constructing differential equations of higher even orders is found, whose solutions are generalized classical orthogonal polynomials. For these polynomials, an explicit image, a three-term recurrence relation, and the appearance of orthogonality conditions with respect to the corresponding distribution function are obtained. The solutions of the corresponding resonance equations are given.

Keywords: and Hermite polynomials, classical orthogonal polynomials, higher-order differential equations, Laguerre, Legendre, orthogonality relation, resonance equations, three-term recurrence relation

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