Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials
In this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension, and Mehler’s formula and its extension for the g...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000499 |
| _version_ | 1797390379192942592 |
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| author | Samaher A. Abdul-Ghani Husam L. Saad |
| author_facet | Samaher A. Abdul-Ghani Husam L. Saad |
| author_sort | Samaher A. Abdul-Ghani |
| collection | DOAJ |
| description | In this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension, and Mehler’s formula and its extension for the generalized q-hypergeometric polynomials. Also demonstrated is a transformational identity involving generating functions for the generalized q-hypergeometric polynomials. |
| first_indexed | 2024-03-08T23:10:52Z |
| format | Article |
| id | doaj.art-d839f9a2120041e0b10f35c6a674af48 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:52Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-d839f9a2120041e0b10f35c6a674af482023-12-15T07:26:43ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100536Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomialsSamaher A. Abdul-Ghani0Husam L. Saad1Department of Mathematics, College of Science, University of Basrah, Basrah, IraqCorresponding author.; Department of Mathematics, College of Science, University of Basrah, Basrah, IraqIn this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension, and Mehler’s formula and its extension for the generalized q-hypergeometric polynomials. Also demonstrated is a transformational identity involving generating functions for the generalized q-hypergeometric polynomials.http://www.sciencedirect.com/science/article/pii/S2666818123000499Generating functionMehler’s formulaRogers formulaA transformational identity |
| spellingShingle | Samaher A. Abdul-Ghani Husam L. Saad Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials Partial Differential Equations in Applied Mathematics Generating function Mehler’s formula Rogers formula A transformational identity |
| title | Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials |
| title_full | Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials |
| title_fullStr | Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials |
| title_full_unstemmed | Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials |
| title_short | Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials |
| title_sort | applications of q difference equation and homogeneous q shift operator rφs dxy in q polynomials |
| topic | Generating function Mehler’s formula Rogers formula A transformational identity |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000499 |
| work_keys_str_mv | AT samaheraabdulghani applicationsofqdifferenceequationandhomogeneousqshiftoperatorrphsdxyinqpolynomials AT husamlsaad applicationsofqdifferenceequationandhomogeneousqshiftoperatorrphsdxyinqpolynomials |