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

Ayman Shehata

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.

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

Abstract

Recently, Shehata et al. [37] introduced the 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, -Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the -Riemann-Liouville and -Weyl fractional integral and derivative operators an extended version of 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, -Konhauser and -Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.
Paper Structure (6 sections, 15 theorems, 97 equations)

This paper contains 6 sections, 15 theorems, 97 equations.

Table of Contents

  1. Introduction
  2. Preliminaries and some definitions
  3. Main Results
  4. Some special cases and applications
  5. Special cases
  6. Conclusion

Key Result

Theorem 2.1

The following relations for $\;_{r+1}R_{s,k}$ hold true and

Theorems & Definitions (38)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Definition 2.1
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • ...and 28 more