Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

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

Highlights
Master Server