{"title":"Conditions for the existence of power solutions to a linear difference equation with constant coefficients","authors":"V. E. Kruglov","doi":"10.26907/0021-3446-2024-4-20-30","DOIUrl":null,"url":null,"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 km\\λk. We present necessary and sufficient conditions on the coefficients of the equation and the initial parameters under which such solutions are obtained.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"21 7","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2024-4-20-30","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 km\λk. 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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