On Polynomial Solutions of Linear Differential Equations with Applications
Kyle R. Bryenton1,
Andrew R. Cameron,
Keegan L. A. Kirk
et al.
Abstract:The analysis of many physical phenomena can be reduced to the study of solutions of differential equations with polynomial coefficients. In the present work, we establish the necessary and sufficient conditions for the existence of polynomial solutions to the linear differential equationfor arbitrary n ≥ 2. We show by example that for n ≥ 3, the necessary condition is not enough to ensure the existence of the polynomial solutions. Using Scheffé's criteria, we show that from this differential equation there are… Show more
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