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An Extended Version of the r+1Rs;k(B;C; z) Matrix Function
Version 1
: Received: 28 December 2023 / Approved: 28 December 2023 / Online: 28 December 2023 (15:17:30 CET)
How to cite: Shehata, A. An Extended Version of the r+1Rs;k(B;C; z) Matrix Function. Preprints 2023, 2023122191. https://doi.org/10.20944/preprints202312.2191.v1 Shehata, A. An Extended Version of the r+1Rs;k(B;C; z) Matrix Function. Preprints 2023, 2023122191. https://doi.org/10.20944/preprints202312.2191.v1
Abstract
Recently, Shehata et al. [37] introduced the r+1Rs(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, di erential 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+1Rs;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-Leer matrix function, k-
Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas
are also discussed.
Keywords
r+1Rs,k(B, C, z) matrix function; k-fractional integral operators; k-fractional derivative operators; Riemann-Liouville k-fractional integral; k-Gamma matrix function; k-Beta matrix function
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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