{"title":"序列的Stieltjes变换所满足的差分方程","authors":"V. Pillwein, D. Dominici","doi":"10.5206/mt.v2i1.14445","DOIUrl":null,"url":null,"abstract":"We study a class of generating functions related to the Stieltjes transform of a sequence of moments with respect to the basis of falling factorial polynomials. Given a recurrence relation for the coefficient sequence, it is shown how to compute the difference equation satisified by its generating function w.r.t. this basis. We give several examples from the class of discrete semiclassical orthogonal polynomials.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Difference equation satisfied by the Stieltjes transform of a sequence\",\"authors\":\"V. Pillwein, D. Dominici\",\"doi\":\"10.5206/mt.v2i1.14445\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a class of generating functions related to the Stieltjes transform of a sequence of moments with respect to the basis of falling factorial polynomials. Given a recurrence relation for the coefficient sequence, it is shown how to compute the difference equation satisified by its generating function w.r.t. this basis. We give several examples from the class of discrete semiclassical orthogonal polynomials.\",\"PeriodicalId\":355724,\"journal\":{\"name\":\"Maple Transactions\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Maple Transactions\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mt.v2i1.14445\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Maple Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mt.v2i1.14445","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Difference equation satisfied by the Stieltjes transform of a sequence
We study a class of generating functions related to the Stieltjes transform of a sequence of moments with respect to the basis of falling factorial polynomials. Given a recurrence relation for the coefficient sequence, it is shown how to compute the difference equation satisified by its generating function w.r.t. this basis. We give several examples from the class of discrete semiclassical orthogonal polynomials.
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