An extended version of the _r+1R_s,k(B,C,z) matrix function

2023/12/28 by Ayman Shehata, Shehata, Ayman
Chemistry · Computer Science · Mathematics · #26A33 #33B15 #33C20 #33C60 #FOS: Mathematics #General Mathematics (math.GM) #Matrix Theory and Algorithms #Spectroscopy and Chemometric Analyses #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2403.09664

openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Shehata et al. [37] introduced the _r+1R_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+1R_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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