Resonant equations and classical orthogonal polynomials

Gawriljuk, IP
1Makarov, VL
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 11:3-10
Section: Mathematics
Language: Ukrainian

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.

Keywords: classical orthogonal polynomials, confluent hypergeometric functions, functions of the second kind, general solution, hypergeometric equation, hypergeometric functions, resonant equation
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