General identities on Bell polynomials

✍ Scribed by Weiping Wang; Tianming Wang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 796 KB
• Volume: 58
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.03.093

✦ Synopsis

The exponential partial Bell polynomials are polynomials in an infinite number of variables x 1 , x 2 , . . . , and it is well-known that some special combinatorial sequences, e.g., Stirling numbers of both kinds, Lah numbers and idempotent numbers, can be obtained from the Bell polynomials. In this paper, we study these polynomials by making appropriate choices of the variables x 1 , x 2 , . . . which are related to associated sequences (binomial sequences) and Sheffer sequences. As a consequence, many general identities on Bell polynomials are proposed. From these general identities, we can obtain series of identities on Bell polynomials. It can also be found that many results presented before are special cases of the general identities of this paper.