Main Article Content
On certain properties and expansions of zeta matrix function, digamma matrix function and polygamma matrix function
Abstract
We introduce the generalized zeta matrix function, digamma matrix function and polygamma matrix function. We obtain the regions of convergence of these matrix functions, some recurrence relations and their integral representations. An identity involving hypergeometric matrix function 3F2 in the form of digamma matrix function is also given.
Mathematics Subject Classification (2010): 15A15, 33B15, 11M06.
Keywords: Generalized zeta function, polygamma function, matrix functional calculus