Modified approach to generalized Stirling numbers via differential operators

B. S. El-Desouky; Nenad P. Cakić; Toufik Mansour

doi:10.1016/j.aml.2009.08.018

Modified approach to generalized Stirling numbers via differential operators

B. S. El-Desouky, Nenad P. Cakić, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we give a modified approach to the generalized Stirling numbers of the second kind S_{r, s} (n, k) and S_{r, s} (k). These numbers were firstly defined by Carlitz and recently studied extensively by Blasiak, Penson and Solomon. This approach depends on the previous results obtained by Carlitz, Toscano and Cakić. We show that Blasiak's results can be investigated from Carlitz and Cakić's results. Some interesting combinatorial identities are obtained.

Original language	English
Pages (from-to)	115-120
Number of pages	6
Journal	Applied Mathematics Letters
Volume	23
Issue number	1
DOIs	https://doi.org/10.1016/j.aml.2009.08.018
State	Published - Jan 2010

Keywords

Boson operators
Combinatorial identities
Generalized Stirling numbers
Normal ordering
Stirling numbers

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2009.08.018

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title = "Modified approach to generalized Stirling numbers via differential operators",

abstract = "In this paper we give a modified approach to the generalized Stirling numbers of the second kind Sr, s (n, k) and Sr, s (k). These numbers were firstly defined by Carlitz and recently studied extensively by Blasiak, Penson and Solomon. This approach depends on the previous results obtained by Carlitz, Toscano and Caki{\'c}. We show that Blasiak's results can be investigated from Carlitz and Caki{\'c}'s results. Some interesting combinatorial identities are obtained.",

keywords = "Boson operators, Combinatorial identities, Generalized Stirling numbers, Normal ordering, Stirling numbers",

author = "El-Desouky, {B. S.} and Caki{\'c}, {Nenad P.} and Toufik Mansour",

year = "2010",

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AU - Cakić, Nenad P.

AU - Mansour, Toufik

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N2 - In this paper we give a modified approach to the generalized Stirling numbers of the second kind Sr, s (n, k) and Sr, s (k). These numbers were firstly defined by Carlitz and recently studied extensively by Blasiak, Penson and Solomon. This approach depends on the previous results obtained by Carlitz, Toscano and Cakić. We show that Blasiak's results can be investigated from Carlitz and Cakić's results. Some interesting combinatorial identities are obtained.

AB - In this paper we give a modified approach to the generalized Stirling numbers of the second kind Sr, s (n, k) and Sr, s (k). These numbers were firstly defined by Carlitz and recently studied extensively by Blasiak, Penson and Solomon. This approach depends on the previous results obtained by Carlitz, Toscano and Cakić. We show that Blasiak's results can be investigated from Carlitz and Cakić's results. Some interesting combinatorial identities are obtained.

KW - Boson operators

KW - Combinatorial identities

KW - Generalized Stirling numbers

KW - Normal ordering

KW - Stirling numbers

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M3 - Article

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SP - 115

EP - 120

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 1

ER -

Modified approach to generalized Stirling numbers via differential operators

Abstract

Keywords

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