{"title":"计算超几何项和的最小伸缩器","authors":"H. Q. Le","doi":"10.1145/569746.569748","DOIUrl":null,"url":null,"abstract":"Let <i>T</i> (<i>n, k</i>) be a hypergeometric term of <i>n</i> and <i>k.</i> We present in this paper an algorithm to construct the minimal telescoper for <i>U</i> (<i>n, k</i>) = ∑<inf><i>m=b</i></inf><sup><i>n</i>-1</sup> <i>T</i> (<i>m, k</i>), <i>b</i> ε ℤ, if it exists. We show a Maple implementation of this method and discuss the problem of finding closed forms of definite sums of <i>U</i> (<i>n, k</i>).","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"210 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computing the minimal telescoper for sums of hypergeometric terms\",\"authors\":\"H. Q. Le\",\"doi\":\"10.1145/569746.569748\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <i>T</i> (<i>n, k</i>) be a hypergeometric term of <i>n</i> and <i>k.</i> We present in this paper an algorithm to construct the minimal telescoper for <i>U</i> (<i>n, k</i>) = ∑<inf><i>m=b</i></inf><sup><i>n</i>-1</sup> <i>T</i> (<i>m, k</i>), <i>b</i> ε ℤ, if it exists. We show a Maple implementation of this method and discuss the problem of finding closed forms of definite sums of <i>U</i> (<i>n, k</i>).\",\"PeriodicalId\":314801,\"journal\":{\"name\":\"SIGSAM Bull.\",\"volume\":\"210 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIGSAM Bull.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/569746.569748\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIGSAM Bull.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/569746.569748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设T (n, k)是n和k的超几何项。本文给出了U (n, k) =∑m=bn-1 T (m, k)， b ε 0的最小望远镜的构造算法，如果它存在。我们给出了该方法的一个Maple实现，并讨论了寻找U (n, k)定和的封闭形式的问题。
Computing the minimal telescoper for sums of hypergeometric terms
Let T (n, k) be a hypergeometric term of n and k. We present in this paper an algorithm to construct the minimal telescoper for U (n, k) = ∑m=bn-1T (m, k), b ε ℤ, if it exists. We show a Maple implementation of this method and discuss the problem of finding closed forms of definite sums of U (n, k).
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