多重调和数在参数修饰阶乘生成序列闭合形式综合中的应用

IF 0.2 Q4 MATHEMATICS, APPLIED

Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI:10.17223/20710410/55/1

I. V. Statsenko

{"title":"多重调和数在参数修饰阶乘生成序列闭合形式综合中的应用","authors":"I. V. Statsenko","doi":"10.17223/20710410/55/1","DOIUrl":null,"url":null,"abstract":"A toolkit and a method for reducing sequences of integers belonging to the class of factorial-generating recursions to a closed form are presented. The signs and properties of the modified factorial-generating recursion of one and two variables are determined. The best-known factorial-generating recursion of two variables is the sequence of Stirling numbers of the first kind. Modified hyperharmonic numbers are used to synthesize an analytical recursion model. The advantages of these numbers for constructing closed forms of factorial-generating recursions are revealed. An incomplete closed form of the sequence of Stirling numbers of the first kind is synthesized.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"APPLICATION OF MULTIHARMONIC NUMBERS FOR THE SYNTHESIS OF CLOSED FORMS OF PARAMETRICALLY MODIFIED FACTORIAL GENERATING SEQUENCES\",\"authors\":\"I. V. Statsenko\",\"doi\":\"10.17223/20710410/55/1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A toolkit and a method for reducing sequences of integers belonging to the class of factorial-generating recursions to a closed form are presented. The signs and properties of the modified factorial-generating recursion of one and two variables are determined. The best-known factorial-generating recursion of two variables is the sequence of Stirling numbers of the first kind. Modified hyperharmonic numbers are used to synthesize an analytical recursion model. The advantages of these numbers for constructing closed forms of factorial-generating recursions are revealed. An incomplete closed form of the sequence of Stirling numbers of the first kind is synthesized.\",\"PeriodicalId\":42607,\"journal\":{\"name\":\"Prikladnaya Diskretnaya Matematika\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Prikladnaya Diskretnaya Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17223/20710410/55/1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Prikladnaya Diskretnaya Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17223/20710410/55/1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

给出了一个工具箱和一种方法，用于将属于阶乘递归类的整数序列约化为封闭形式。确定了一变量和二变量的改进阶乘递归的符号和性质。最著名的两个变量的产生阶乘的递归是第一类斯特林数序列。利用修正超调和数合成了一个解析递推模型。揭示了这些数在构造阶乘生成递归的封闭形式时的优点。综合了第一类斯特林数序列的不完全封闭形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

APPLICATION OF MULTIHARMONIC NUMBERS FOR THE SYNTHESIS OF CLOSED FORMS OF PARAMETRICALLY MODIFIED FACTORIAL GENERATING SEQUENCES

A toolkit and a method for reducing sequences of integers belonging to the class of factorial-generating recursions to a closed form are presented. The signs and properties of the modified factorial-generating recursion of one and two variables are determined. The best-known factorial-generating recursion of two variables is the sequence of Stirling numbers of the first kind. Modified hyperharmonic numbers are used to synthesize an analytical recursion model. The advantages of these numbers for constructing closed forms of factorial-generating recursions are revealed. An incomplete closed form of the sequence of Stirling numbers of the first kind is synthesized.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Prikladnaya Diskretnaya Matematika MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

50.00%

发文量

期刊介绍： The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]