An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911798412705792 |
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| author | Shehata, Ayman |
| author_facet | Shehata, Ayman |
| contents | Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, differential properties, new integral representations, $k$-Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the $k$-Riemann-Liouville and $k$-Weyl fractional integral and derivative operators an extended version of $_{r+1}R_{s,k}$ matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leffer matrix function, $k$-Konhauser and $k$-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function Shehata, Ayman General Mathematics 26A33, 33B15, 33C20, 33C60 Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, differential properties, new integral representations, $k$-Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the $k$-Riemann-Liouville and $k$-Weyl fractional integral and derivative operators an extended version of $_{r+1}R_{s,k}$ matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leffer matrix function, $k$-Konhauser and $k$-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed. |
| title | An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function |
| topic | General Mathematics 26A33, 33B15, 33C20, 33C60 |
| url | https://arxiv.org/abs/2403.09664 |