Best web design - 332 ARITHMETIC 4.5.2 An analysis of the lattice-point
332 ARITHMETIC 4.5.2 An analysis of the lattice-point model can be carried out by solving the following rather complicated set of double recurrence relations: 1 &, = a + 5&qm–2) + … -I LA,o &, ifm 2 1; 2m-l + A mn = c + iAcrn-~jn + … + &&AI, + &hn, if m > 72 2 0; A mn - &V2, if n > m 2 0. (34) The problem is to solve for A,, in terms of m, n, and the parameters a, b, c, and Aoo. This is an interesting set of recurrence equations, which have an interesting solution. First we observe that if 0 5 rz < m, A(,+,),= c+ c 2-kA(m+,-k), + 2-m&n l