Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0913.05006
Hsu, Leetsch C.; Shiue, Peter Jau-Shyong
A unified approach to generalized Stirling numbers. (English)
[J] Adv. Appl. Math. 20, No.3, 366-384 (1998). ISSN 0196-8858

Set $(z| \alpha)_n =z(z-\alpha) \cdots (z-n \alpha+ \alpha)$ and $(z | \alpha)_0=1$. For complex parameters $(\alpha, \beta,r) \ne(0,0,0)$, the paper studies the inverse relations $$(t|\alpha)_n=\sum^n_{k=0} S^1(n,k) (t-r | \beta)_k \quad \text {and} \quad (t | \beta)_n =\sum^n_{k=0} S^2(n,k) (t+r | \alpha)_k.$$ The resulting generalized Stirling numbers include binomial coefficients, Lah numbers, signless Stirling numbers, and many other generalized Stirling numbers. Generating functions and Dobinski-type formulae are also given.
[L.A.Székely (Columbia/South Carolina)]

MSC 2000:: *05A15 Combinatorial enumeration problems
11B73 Bell and Stirling numbers

Keywords: generating functions; Stirling numbers; binomial coefficients; Lah numbers

Cited in: Zbl 1065.05018 Zbl 1099.11007 Zbl 1101.11312 Zbl 1036.11004 Zbl 0992.11023

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]