{"title":"Conditions for the Existence of Power Solutions to a Linear Difference Equation with Constant Coefficients","authors":"V. E. Kruglov","doi":"10.3103/s1066369x24700245","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 <span>\\({{k}^{m}}{{\\lambda }^{k}}\\)</span>. We present necessary and sufficient conditions on the coefficients of the equation and the initial parameters under which such solutions are obtained.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"40 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700245","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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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