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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| Language: | English |
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De Gruyter
2024-12-01
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| Series: | Demonstratio Mathematica |
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| 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. |
| format | Article |
| id | doaj-art-fbfb38e59f0b4b60b97c50ee62b77a8f |
| institution | OA Journals |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| 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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