656 ANSWERS TO EXERCISES 4.7 2. (Mac os x web server) We have
656 ANSWERS TO EXERCISES 4.7 2. We have Vt+ w, = vo u, -(V, Wo)(V, -1%) -(V, Wl)(VJ- IL,) -. . * - (V, W,-,)(I@ ,). Thus, we can start by replacing (Uj, V,) by (ViUj, Vi- V,) for j 2 1, then set W, +-U, -xOck<,, wkvn-k for n 2 0, finally replace Wj by W,lVo 3+1 for j > 0 Similar techniques are possible in connection with other algorithms -. in this section. 3. Yes. When LY = 0, it is easy to prove by induction that WI = Wz = . .. = 0. When cy = 1, we find W, = V,, by the cute identity k -(n -k) &l/n-k = v,v,. n 4. If W(z) = ev( ), then W (z) = V (z)W(z); we find WO = 1, and wn = c ;vkw,-k, for n 2 1. l