{"title":"常数线性差分方程幂级数解存在的条件","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":"{\"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}","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}
Conditions for the existence of power solutions to a linear difference equation with constant coefficients
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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