{"title":"一种广义Apagodu-Zeilberger算法","authors":"Shaoshi Chen, Manuel Kauers, C. Koutschan","doi":"10.1145/2608628.2608641","DOIUrl":null,"url":null,"abstract":"The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary Δ-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper Δ-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"A generalized Apagodu-Zeilberger algorithm\",\"authors\":\"Shaoshi Chen, Manuel Kauers, C. Koutschan\",\"doi\":\"10.1145/2608628.2608641\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary Δ-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper Δ-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.\",\"PeriodicalId\":243282,\"journal\":{\"name\":\"International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2608628.2608641\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2608628.2608641","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary Δ-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper Δ-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.
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