Further investigations on the two variables second Appell hypergeometric matrix function. Issue 3 (4th March 2023) - Abdalla, Mohamed; Abd-Elmageed, Hala; Abul-Ez, Mahmoud; Zayed, Mohra
Abstract: Over the last two decades, special matrix functions have become a major area of study for mathematicians and physicists. The famous four Appell hypergeometric matrix functions have received considerable attention by many authors from diﬀerent points of view. The present paper is devoted to provide further investigations on the two variables second Appell hypergeometric matrix functions. Precisely, we derive certain mathematical properties such as limit formulae of Humbert hypergeometric matrix functions, recursion formulae using contiguous matrix relations, some diﬀerentiation and summation formulae. We also find general diﬀerential operators which induce some diﬀerential equations. This enriches the theory of special matrix functions. The obtained results are believed to be newly presented.