Applicable Analysis and Discrete Mathematics | |
COMBINATORIAL IDENTITIES INVOLVING THE CENTRAL COEFFICIENTS OF A SHEFFER MATRIX | |
article | |
Emanuele Munarini1  | |
[1] Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32 | |
关键词: $r$-Lah numbers; $r$-Stirling numbers; Appell sequences; Sheffer sequences; Combinatorial Identities; | |
DOI : 10.2298/AADM180226017M | |
学科分类:社会科学、人文和艺术(综合) | |
来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering | |
【 摘 要 】
Given m ∈ N, m ≥ 1, and a Sheffer matrix S = [sn,k]n,k≥0, we obtain the exponential generating series for the coefficients a+(m+1)na+mn −1 sa+(m+1)n,a+mn.Then, by using this series, we obtain two general combinatorial identities, and their specialization to r-Stirling, r-Lah and r-idempotent numbers. In particular, using this approach, we recover two well known binomial identities, namely Gould’s identity and Hagen-Rothe’s identity. Moreover, wegeneralize these results obtaining an exchange identity for a cross sequence(or for two Sheffer sequences) and an Abel-like identity for a cross sequence(or for an s-Appell sequence).
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202307080003741ZK.pdf | 468KB | download |