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

Key words:

• Generalized zeta function
• polygamma function
• matrix functional calculus