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arXiv · 2403.09664

An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function

Ayman Shehata
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Abstract

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.

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BibTeXRIS

Ayman Shehata. 2023-12-28. An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function. https://arxiv.org/abs/2403.09664

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