Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations
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.
How to Cite
Bandyrskii, B. I., V. L. Makarov, and N. M. Romaniuk. “Generalization of Resonance Equations for the Laguerre- and Legendre-Type Polynomials to the Fourth-Order Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 11, Nov. 2019, pp. 1529-38, http://umj.imath.kiev.ua/index.php/umj/article/view/1533.