Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers
In this paper, type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semanti...
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MDPI AG
2021-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/4/343 |
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| author | Roberto Corcino Mary Ann Ritzell Vega Amerah Dibagulun |
| author_facet | Roberto Corcino Mary Ann Ritzell Vega Amerah Dibagulun |
| author_sort | Roberto Corcino |
| collection | DOAJ |
| description | In this paper, type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogues of the <i>r</i>-Whitney numbers of the second kind is defined and a combinatorial interpretation in the context of the <i>A</i>-tableaux is given. Moreover, some convolution-type identities, which are useful in deriving the Hankel transform of the type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogue of the <i>r</i>-Whitney numbers of the second kind are obtained. Finally, the Hankel transform of the type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogue of the <i>r</i>-Dowling numbers are established. |
| first_indexed | 2024-03-10T04:34:19Z |
| format | Article |
| id | doaj.art-05c4ea1162484fc7a8cf8cc505db0a44 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:34:19Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-05c4ea1162484fc7a8cf8cc505db0a442023-11-23T03:50:22ZengMDPI AGAxioms2075-16802021-12-0110434310.3390/axioms10040343Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling NumbersRoberto Corcino0Mary Ann Ritzell Vega1Amerah Dibagulun2Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City 6000, PhilippinesDepartment of Mathematics and Statistics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, PhilippinesDepartment of Mathematics, Mindanao State University-Main Campus, Marawi City 9700, PhilippinesIn this paper, type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogues of the <i>r</i>-Whitney numbers of the second kind is defined and a combinatorial interpretation in the context of the <i>A</i>-tableaux is given. Moreover, some convolution-type identities, which are useful in deriving the Hankel transform of the type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogue of the <i>r</i>-Whitney numbers of the second kind are obtained. Finally, the Hankel transform of the type 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogue of the <i>r</i>-Dowling numbers are established.https://www.mdpi.com/2075-1680/10/4/343<i>r</i>-Whitney numbers<i>r</i>-Dowling numbersA-tableauxconvolution identitiesbinomial transformHankel transform |
| spellingShingle | Roberto Corcino Mary Ann Ritzell Vega Amerah Dibagulun Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers Axioms <i>r</i>-Whitney numbers <i>r</i>-Dowling numbers A-tableaux convolution identities binomial transform Hankel transform |
| title | Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers |
| title_full | Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers |
| title_fullStr | Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers |
| title_full_unstemmed | Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers |
| title_short | Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers |
| title_sort | hankel transform of the type 2 i p i i q i analogue of i r i dowling numbers |
| topic | <i>r</i>-Whitney numbers <i>r</i>-Dowling numbers A-tableaux convolution identities binomial transform Hankel transform |
| url | https://www.mdpi.com/2075-1680/10/4/343 |
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