SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND FOR SOME SEQUENCES AND FUNCTIONS

Feng Qi (1, 2, 3, 4) , Da-Wei Niu (5) , Dongkyu Lim (6) , Yong-Hong Yao (3)

1 Henan Polytechnic University
2 Tianjin Polytechnic University
3 UESTC - University of Electronic Science and Technology of China [Chengdu]
4 Inner Mongolia University for Nationalities
5 ECNU - East China Normal University [Shangaï]
6 SKKU - Sungkyunkwan University [Suwon]

In the paper, the authors concisely review some closed formulas and applications of special values of the Bell polynomials of the second kind for some special sequences and elementary functions, explicitly present closed formulas for those sequences investigated in [F. T. Howard, A special class of Bell polynomials, Math. Comp. 35 (1980), no. 151, 977–989; Available online at https://doi.org/10.2307/2006208], and newly establish some closed formulas for some special values of the Bell polynomials of the second kind.

Mots clés: review; closed formula; special value; Bell polynomial of the second kind; sequence; elementary function; application

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Analyse classique [math.CA]

Feng Qi, Da-Wei Niu, Dongkyu Lim, Yong-Hong Yao. SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND FOR SOME SEQUENCES AND FUNCTIONS: Special values of Bell polynomials of second kind. 2018. ⟨hal-01766566v1⟩