Some Relations on the <i>_rR_s</i>(<i>P</i>,<i>Q</i>,<i>z</i>) Matrix Function

Abstract

In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationship with other generalized special matrix functions in the context of the Konhauser and Laguerre matrix polynomials.

Keywords

• <i>_rR_s</i>(<i>P</i>,<i>Q</i>,<i>z</i>) matrix function
• recurrence relation
• integral representation
• generalized (Wright) hypergeometric matrix functions
• Mittag–Leffler matrix function
• fractional integral