Узагальнення резонансних рівнянь для поліномів типу Лагерра і Лежандра на рівняння четвертого порядку
Abstract
UDC 517.587 A recurrent algorithm for finding particular solutions of а fourth-order resonance equation connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of partial solutions of resonance equations in Banach spaces, which was proved by V. L. Makarov in 1976. An example of general solution to the resonant equations with a differential operator for the Laguerre-type polynomials is presented.
Fields of Study & Subjects
Mathematical functions and polynomials
Spectral Theory in Mathematical Physics
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 71
- Issue
- 11
- Pages
- 1529–1538
- Publication date
- 9 February 2026
- Language
- UK