Some inequalities for the Bell numbers |
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| Authors: | Feng Qi |
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| Affiliation: | 1.Institute of Mathematics,Henan Polytechnic University,Jiaozuo City,China;2.College of Mathematics,Inner Mongolia University for Nationalities,Tongliao City,China;3.Department of Mathematics, College of Science,Tianjin Polytechnic University,Tianjin City,China |
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| Abstract: | In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers. |
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