To find constant g 0, we perform summation over equation (A 9): ∑ k = 0 N − 1 g k = ∑ k = 0 N − 1 f k − ∑ k = 0 N − 1 f k + 1 = f 0 − f 1 + f 1 − f 2 + ⋯ + f N − 1 − f N = f 0 − f N = 1.
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 ).