Differential equation of minimal order for a system of polynomials

UDC 517.92, 517.58 Classical orthogonal polynomials, such as Laguerre, Legendre, Hermite, Hegenbauer, Jacobi, and Bessel polynomials, served as a fundamental tool for solving applied problems. They satisfy second-order differential equations. It is of interest to analyze the questions concerning the...

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Бібліографічні деталі
Дата:2026
Автори: Makarov, V., Kashpur, O., Макаров, Володимир, Кашпур, Олена
Формат: Стаття
Мова:Українська
Опубліковано: Institute of Mathematics, NAS of Ukraine 2026
Онлайн доступ:https://umj.imath.kiev.ua/index.php/umj/article/view/9891
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
Опис
Резюме:UDC 517.92, 517.58 Classical orthogonal polynomials, such as Laguerre, Legendre, Hermite, Hegenbauer, Jacobi, and Bessel polynomials, served as a fundamental tool for solving applied problems. They satisfy second-order differential equations. It is of interest to analyze the questions concerning the minimal order of equations of this kind: Is it possible that these polynomials are solutions of the first-order equations and what equations of the minimal order are satisfied by other polynomials, in particular, by the reciprocal classical polynomials. The present paper is devoted to the analysis of these problems.
DOI:10.3842/umzh.v78i3-4.9891