A 19 It is convenient to rewrite the summation in the following form ∑ l = 0 n − 1 x l f n − l ( n − l ) = ∑ l = 1 n x n − l f l l. A 20 Solution of the recurrence relation K n = b n+1 − b n takes the form b n = ∑ j = 0 n − 1 K j.
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 ).