A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers

In this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of λ\lambda -analogue of Lah numbers arising from degenerat...

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Main Authors: Kim Taekyun, Kim Hye Kyung
Format: Article
Language:English
Published: De Gruyter 2024-12-01
Series:Demonstratio Mathematica
Subjects:
Online Access:https://doi.org/10.1515/dema-2024-0065
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author Kim Taekyun
Kim Hye Kyung
author_facet Kim Taekyun
Kim Hye Kyung
author_sort Kim Taekyun
collection DOAJ
description In this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of λ\lambda -analogue of Lah numbers arising from degenerate differential operators. Using these new identities, we study the normal ordering of degenerate integral power of the number operator in terms of boson operators, which is represented by means of λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers, respectively.
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spelling doaj-art-fbfb38e59f0b4b60b97c50ee62b77a8f2025-08-20T02:38:26ZengDe GruyterDemonstratio Mathematica2391-46612024-12-01571518810.1515/dema-2024-0065A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbersKim Taekyun0Kim Hye Kyung1Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDepartment of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of KoreaIn this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of λ\lambda -analogue of Lah numbers arising from degenerate differential operators. Using these new identities, we study the normal ordering of degenerate integral power of the number operator in terms of boson operators, which is represented by means of λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers, respectively.https://doi.org/10.1515/dema-2024-0065lah numbersdegenerate stirling numbers of the second kinddegenerate differential operatornormal orderingnumber operator05a1705a1811b73
spellingShingle Kim Taekyun
Kim Hye Kyung
A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
Demonstratio Mathematica
lah numbers
degenerate stirling numbers of the second kind
degenerate differential operator
normal ordering
number operator
05a17
05a18
11b73
title A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
title_full A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
title_fullStr A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
title_full_unstemmed A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
title_short A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
title_sort note on λ analogue of lah numbers and λ analogue of r lah numbers
topic lah numbers
degenerate stirling numbers of the second kind
degenerate differential operator
normal ordering
number operator
05a17
05a18
11b73
url https://doi.org/10.1515/dema-2024-0065
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