恒系数线性微分方程幂级数解存在的条件

IF 0.5 Q3 MATHEMATICS Russian Mathematics Pub Date : 2024-08-06 DOI:10.3103/s1066369x24700245

V. E. Kruglov

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引用次数: 0

摘要

摘要借助具有常数系数的差分方程的一般解公式，证明该方程的解集包含 \({{k}^{m}}{{{\lambda }^{k}}\) 类型的经典解。我们提出了获得此类解的方程系数和初始参数的必要条件和充分条件。

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Conditions for the Existence of Power Solutions to a Linear Difference Equation with Constant Coefficients

Abstract

With the help of the formula for the general solution of a difference equation with constant coefficients, it is shown that the set of solutions to this equation contains classical solutions of the type \({{k}^{m}}{{\lambda }^{k}}\). We present necessary and sufficient conditions on the coefficients of the equation and the initial parameters under which such solutions are obtained.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.