A unified approach to generalized Stirling numbers
type: Item
instance of: scholarly article
title: A unified approach to generalized Stirling numbers
zbMATH Open document ID: 0913.05006
author: Leetsch C. Hsu
author: Peter J.-S. Shiue
published in: Advances in Applied Mathematics
publication date: 1999-06-08T00:00:00Z
review text: Set \((z| \alpha)_n =z(z-\alpha) \cdots (z-n \alpha+ \alpha)\) and \((z | \alpha)_0=1\). For complex parameters \((\alpha, \beta,r) \neq(0,0,0)\), 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.
reviewed by: László A. Székely
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 1221690
zbMATH Keywords: generating functions
zbMATH Keywords: Stirling numbers
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Lah numbers
MaRDI profile type: Publication
full work available at URL: aama.1998.0586
OpenAlex ID: W2038339694
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DOI: 10.1006/AAMA.1998.0586
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description: scientific article; zbMATH DE number 1221690