Some Kazhdan-Lusztig Coefficients of Affine Weyl Group of Type (B)over-tilde2

Let (W, S) be the affine Weyl group of type (B) over tilde (2), on which we consider the length function l from W to N and the Bruhat order <=. For y < w in W, let mu(y,w) be the coefficient of q(1/2(l(w)-l(y)-1) in Kazhdan-Lusztig polynomial P-y,P-w is an element of Z[q]. We determine some mu(y, w) for y is an element of c(0) and w is an element of c(2), where c(0) is the lowest two-sided cell of <(B)over tilde>(2) and c(2) is the higher one. Furthermore, we get some consequences using left or right strings and some properties of leading coefficients.