Some identities of Bell polynomials

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• 作者：Dae San Kim ; Taekyun Kim
• 关键词：Bell ; polynomial ; umbral calculus ; poly ; Bernoulli polynomial ; higher ; order Bernoulli polynomial ; Cauchy polynomial ; 05A19 ; 05A40 ; 11B73 ; 11B83
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：58
• 期：10
• 页码：1-10
• 全文大小：143 KB
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• 作者单位：Dae San Kim (1)
  Taekyun Kim (2)
  
  1. Department of Mathematics, Sogang University, Seoul, 121-742, Republic of Korea
  2. Department of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

We investigate Bell polynomials, also called Touchard polynomials or exponential polynomials, by using and without using umbral calculus. We use three different formulas in order to express various known families of polynomials such as Bernoulli polynomials, poly-Bernoulli polynomials, Cauchy polynomials and falling factorials in terms of Bell polynomials and vice versa. In addition, we derive several properties of Bell polynomials along the way. Keywords Bell-polynomial umbral calculus poly-Bernoulli polynomial higher-order Bernoulli polynomial Cauchy polynomial