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

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