Resonant equations and classical orthogonal polynomials

TitleResonant equations and classical orthogonal polynomials
Publication TypeJournal Article
Year of Publication2018
AuthorsGawriljuk, IP, Makarov, VL
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.11.003
Issue11
SectionMathematics
Pagination3-10
Date Published11/2018
LanguageUkrainian
Abstract

Using the general theorem by V.L. Makarov on the representation of particular solutions of the resonant equation in Banach spaces (1974), the authors propose and justify an recurrent algorithm for particular solutions of the resonant equations of the first and second kinds with the general differential operator defining the classical orthogonal polynomials. An example of the general solution of the resonant equations with the differential Legendre operator is given.

Keywordsclassical orthogonal polynomials, confluent hypergeometric functions, functions of the second kind, general solution, hypergeometric equation, hypergeometric functions, resonant equation
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