Recurrence for probabilistic extension of Dowling polynomials
Spivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic Dowling polynomials associated with YY and als...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-05-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0150 |
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| _version_ | 1849737059881713664 |
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| author | Ma Yuankui Kim Taekyun Kim Dae San Xu Rongrong |
| author_facet | Ma Yuankui Kim Taekyun Kim Dae San Xu Rongrong |
| author_sort | Ma Yuankui |
| collection | DOAJ |
| description | Spivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic Dowling polynomials associated with YY and also that for the probabilistic rr-Dowling polynomials associated with YY. Here YY is a random variable whose moment generating function exists in a neighborhood of the origin. |
| format | Article |
| id | doaj-art-c6c239592b444be2a6706d3d68c6f78a |
| institution | DOAJ |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-c6c239592b444be2a6706d3d68c6f78a2025-08-20T03:07:04ZengDe GruyterOpen Mathematics2391-54552025-05-0123151010.1515/math-2025-0150Recurrence for probabilistic extension of Dowling polynomialsMa Yuankui0Kim Taekyun1Kim Dae San2Xu Rongrong3School of Science, Xi’an Technological University, Xi’an, 710021, Shaanxi, P. R. ChinaDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDepartment of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaSchool of Science, Xi’an Technological University, Xi’an, 710021, Shaanxi, P. R. ChinaSpivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic Dowling polynomials associated with YY and also that for the probabilistic rr-Dowling polynomials associated with YY. Here YY is a random variable whose moment generating function exists in a neighborhood of the origin.https://doi.org/10.1515/math-2025-0150probabilistic whitney numbers of the second kindprobabilistic dowling polynomialsprobabilistic r-whitney numbers of the secondprobabilistic r-dowling polynomials11b7311b83 |
| spellingShingle | Ma Yuankui Kim Taekyun Kim Dae San Xu Rongrong Recurrence for probabilistic extension of Dowling polynomials Open Mathematics probabilistic whitney numbers of the second kind probabilistic dowling polynomials probabilistic r-whitney numbers of the second probabilistic r-dowling polynomials 11b73 11b83 |
| title | Recurrence for probabilistic extension of Dowling polynomials |
| title_full | Recurrence for probabilistic extension of Dowling polynomials |
| title_fullStr | Recurrence for probabilistic extension of Dowling polynomials |
| title_full_unstemmed | Recurrence for probabilistic extension of Dowling polynomials |
| title_short | Recurrence for probabilistic extension of Dowling polynomials |
| title_sort | recurrence for probabilistic extension of dowling polynomials |
| topic | probabilistic whitney numbers of the second kind probabilistic dowling polynomials probabilistic r-whitney numbers of the second probabilistic r-dowling polynomials 11b73 11b83 |
| url | https://doi.org/10.1515/math-2025-0150 |
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