A 16 This recurrence relations can be simplified as 1 λ f n n = x K n − 1 − K n, A 17 where K n = b n + 1 − b n. A 18 It can be shown that the solution of equation (A 17) is given by K n = x n K 0 − 1 λ ∑ l = 0 n − 1 x l f n − l ( n − l ).
A 4 Rearranging terms yields − s 2 b n n + s ( f n n − b n ( λ + ϕ ) ) + ( λ + ϕ ) f n = ϕ f n − 1 + λ f n + 1 − s ( ϕ b n − 1 + λ b n + 1 ).