An infinite class of completely monotonic functions involving the qq-gamma function

In this paper, the qq-analogue of the Stirling formula for the qq-gamma function is used to prove the complete monotonicity property for an infinite class of functions which are all closely related to the qq-gamma function and its logarithmic derivatives (qq-polygamma functions). As an application of this result, the two-sided inequalities for the qq-gamma and the qq-polygamma functions are established.