Differential equation of minimal order for a system of polynomials
DOI:
https://doi.org/10.3842/umzh.v78i3-4.9891Keywords:
Polynomial differential equation, minimal order differential equation, classical orthogonal polynomials, Bessel polynomials, recurrence relationAbstract
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.
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