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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18612 |
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| _version_ | 1866917878946594816 |
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| author | Alqahtani, Awatif Muflih Yousuf, Saleem Wani, Shahid Ahmad Costas-Santos, Roberto S. |
| author_facet | Alqahtani, Awatif Muflih Yousuf, Saleem Wani, Shahid Ahmad Costas-Santos, Roberto S. |
| contents | This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining consistent with established findings. The primary focus of this study is the introduction of degenerate multidimensional Hermite-based Appell polynomials (DMHAP), denoted as ${}_{\mathbb{H}}\mathbb{A}^{[r]}_n(l_1, l_2, l_3, \dots, l_r; \vartheta)$. These DMHAP form essential families of orthogonal polynomials, demonstrating strong connections with classical Hermite and Appell polynomials. Additionally, we derive symmetric identities and examine the fundamental properties of these polynomials. Finally, we establish an operational framework to investigate and develop these polynomials further. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications Alqahtani, Awatif Muflih Yousuf, Saleem Wani, Shahid Ahmad Costas-Santos, Roberto S. General Mathematics 33E20, 33C45, 33B10, 33E30, 11T23 This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining consistent with established findings. The primary focus of this study is the introduction of degenerate multidimensional Hermite-based Appell polynomials (DMHAP), denoted as ${}_{\mathbb{H}}\mathbb{A}^{[r]}_n(l_1, l_2, l_3, \dots, l_r; \vartheta)$. These DMHAP form essential families of orthogonal polynomials, demonstrating strong connections with classical Hermite and Appell polynomials. Additionally, we derive symmetric identities and examine the fundamental properties of these polynomials. Finally, we establish an operational framework to investigate and develop these polynomials further. |
| title | Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications |
| topic | General Mathematics 33E20, 33C45, 33B10, 33E30, 11T23 |
| url | https://arxiv.org/abs/2412.18612 |