PRECISE RATE IN THE LAW OF ITERATED LOGARITHM FOR ρ-MIXING SEQUENCE

2(b+1),if b≥0.It is proved that,for any b>-1,lime^2(b+1) e→0^∞∑n=1(log logn)^b/nlognP{Mn≥eσ√2nlog logn}=2/(b+1)√πГ(b+3/2)^∞∑k=0(-1)^k/(2k+1)^2b+2,where Г(·)is a Gamma function.