PSI, POLYGAMMA FUNCTIONS AND Q-COMPLETE MONOTONICITY ON TIME SCALES

In this paper, we generalize psi and polygamma functions based on the Laplace transform in the field of time scales, and explore some prop-erties of them. Next, we present the concepts of q-complete monotonicity, q-logarithmically complete monotonicity and q-absolute monotonicity with delta derivative on time scales. At last, we prove that the functions  & alpha;& psi;R0,T(s) - ln s + 2s 1 + 1 12s2is 1-complete monotonicity on (0, oo) if T = N and & alpha; E [ 3-2 & RADIC;3 6 , 3+2 & RADIC;3 6 ], and it is decreasing on (0, oo) if T = hN U {1}(h > 1) and & alpha; = 1, where R0 = [0, oo) and & psi;R0,T is a psi function on time scales.