Abstract: Let {X_n, n≥1} be a strictly stationary sequence of ρ-mixing random variables. Using the central limit theorem and moment inequality of ρ-mixing random sequences, under suitable conditions, we gave general function formula for the precise asymptotics of  the complete moment convergence of the  partial sums  for ρ-mixing random variable sequences in the logarithm law.

Key words: complete moment convergence, ρ-mixing  sequence, precise asymptotics