Some inequalities for the Bell numbers
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.
FENG QI1 2 3
Volume 132, 2022
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode