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Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities

Siqintuya Jin1, Bai-Ni Guo2,*, Feng Qi3,*

1 College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, 028043, China
2 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, China
3 School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

* Corresponding Authors: Bai-Ni Guo. Email: email; Feng Qi. Email: email

(This article belongs to the Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 132(3), 781-799. https://doi.org/10.32604/cmes.2022.019941

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.

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APA Style
Jin, S., Guo, B., Qi, F. (2022). Partial bell polynomials, falling and rising factorials, stirling numbers, and combinatorial identities. Computer Modeling in Engineering & Sciences, 132(3), 781-799. https://doi.org/10.32604/cmes.2022.019941
Vancouver Style
Jin S, Guo B, Qi F. Partial bell polynomials, falling and rising factorials, stirling numbers, and combinatorial identities. Comput Model Eng Sci. 2022;132(3):781-799 https://doi.org/10.32604/cmes.2022.019941
IEEE Style
S. Jin, B. Guo, and F. Qi "Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities," Comput. Model. Eng. Sci., vol. 132, no. 3, pp. 781-799. 2022. https://doi.org/10.32604/cmes.2022.019941



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