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

TitleHigher-order differential equations with polynomial solutions associated with classical orthogonal polynomials
Publication TypeJournal Article
Year of Publication2020
AuthorsMakarov, VL
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2020.07.003
Issue7
SectionMathematics
Pagination3-9
Date Published7/2020
LanguageUkrainian
Abstract

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.

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