{"title":"Touchard多项式和贝尔数的显式上限","authors":"A.-M. Acu, J. A. Adell, I. Raşa","doi":"10.1007/s10474-024-01401-6","DOIUrl":null,"url":null,"abstract":"<p>We obtain explicit upper bounds for the Touchard polynomials\n<span>\\(T_n(x)\\)</span>, for <span>\\(x>0\\)</span>. When applied to the Bell numbers <span>\\(B_n=T_n(1)\\)</span>, such bounds\nare asymptotically sharp. A simple probabilistic approach based on estimates\nof moments of nonnegative random variables is used. Applications giving upper\nbounds for the moments of a certain subset of Jakimovski-Leviatan operators are\nalso provided.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Explicit upper bounds for Touchard polynomials and Bell numbers\",\"authors\":\"A.-M. Acu, J. A. Adell, I. Raşa\",\"doi\":\"10.1007/s10474-024-01401-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We obtain explicit upper bounds for the Touchard polynomials\\n<span>\\\\(T_n(x)\\\\)</span>, for <span>\\\\(x>0\\\\)</span>. When applied to the Bell numbers <span>\\\\(B_n=T_n(1)\\\\)</span>, such bounds\\nare asymptotically sharp. A simple probabilistic approach based on estimates\\nof moments of nonnegative random variables is used. Applications giving upper\\nbounds for the moments of a certain subset of Jakimovski-Leviatan operators are\\nalso provided.</p>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10474-024-01401-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01401-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Explicit upper bounds for Touchard polynomials and Bell numbers
We obtain explicit upper bounds for the Touchard polynomials
\(T_n(x)\), for \(x>0\). When applied to the Bell numbers \(B_n=T_n(1)\), such bounds
are asymptotically sharp. A simple probabilistic approach based on estimates
of moments of nonnegative random variables is used. Applications giving upper
bounds for the moments of a certain subset of Jakimovski-Leviatan operators are
also provided.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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