A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula>
In this paper, we introduce <i>q</i>-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic <i>p</i>-adic <i>q</i>-integrals on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline&q...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/6/1119 |
| _version_ | 1797482052827742208 |
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| author | Waseem A. Khan |
| author_facet | Waseem A. Khan |
| author_sort | Waseem A. Khan |
| collection | DOAJ |
| description | In this paper, we introduce <i>q</i>-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic <i>p</i>-adic <i>q</i>-integrals on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, we also find a few new identities and results of this type of polynomials and numbers. |
| first_indexed | 2024-03-09T22:22:48Z |
| format | Article |
| id | doaj.art-10519507e97242b98e5824372d0002e8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:48Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-10519507e97242b98e5824372d0002e82023-11-23T19:11:08ZengMDPI AGSymmetry2073-89942022-05-01146111910.3390/sym14061119A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula>Waseem A. Khan0Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi ArabiaIn this paper, we introduce <i>q</i>-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic <i>p</i>-adic <i>q</i>-integrals on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, we also find a few new identities and results of this type of polynomials and numbers.https://www.mdpi.com/2073-8994/14/6/1119<i>q</i>-Catalan numbers<i>q</i>-analogue of degenerate Catalan polynomials and numbersStirling numbers |
| spellingShingle | Waseem A. Khan A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> Symmetry <i>q</i>-Catalan numbers <i>q</i>-analogue of degenerate Catalan polynomials and numbers Stirling numbers |
| title | A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> |
| title_full | A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> |
| title_fullStr | A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> |
| title_full_unstemmed | A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> |
| title_short | A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> |
| title_sort | note on i q i analogue of degenerate catalan numbers associated with i p i adic integral on inline formula math display inline semantics msub mi mathvariant double struck z mi mi p mi msub semantics math inline formula |
| topic | <i>q</i>-Catalan numbers <i>q</i>-analogue of degenerate Catalan polynomials and numbers Stirling numbers |
| url | https://www.mdpi.com/2073-8994/14/6/1119 |
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