Abstract
The symmetric patterns that inequalities contain are reflected in researchers' studies in many mathematical sciences. In this paper, we prove an asymptotic expansion for the generalized gamma function Gamma(mu)(v) and study the completely monotonic (CM) property of a function involving Gamma(mu)(v) and the generalized digamma function psi(mu)(v). As a consequence, we establish some bounds for Gamma(mu)(v), psi(mu)(v) and polygamma functions psi((r))(mu)(v), r >= 1.