An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions - Guo, Bai-Ni; Qi, Feng (Global Journal of Mathematical Analysis, 2014)
In the paper, by two methods, the authors find an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind. Moreover, the authors supply an alternative proof of the well-known ``triangular'' recurrence relation for Stirling numbers of the second kind. In a remark, the authors reveal the combinatorial interpretation of the special values for Kummer confluent hypergeometric functions and the total sum of Lah numbers.Keywords:Â explicit formula; Bell number; conuent hypergeometric function of the first kind; Stirling number of the second kind; combinatorial interpretation; alternative proof; recurrence relation; polylogarithm