Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities
Siqintuya Jin1, Bai-Ni Guo2,*, Feng Qi3,*
CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 781-799, 2022, DOI:10.32604/cmes.2022.019941
- 27 June 2022
(This article belongs to the Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)
Abstract In the paper, the authors collect, discuss, and find out several connections, equivalences, closed-form formulas, and
combinatorial identities concerning partial Bell polynomials, falling factorials, rising factorials, extended binomial
coefficients, and the Stirling numbers of the first and second kinds. These results are new, interesting, important,
useful, and applicable in combinatorial number theory. More >