A 5 Equating coefficients of s on both sides yields two recurrence relations ( λ + ϕ ) f n = ϕ f n − 1 + λ f n + 1 A 6 and f n n − ( λ + ϕ ) b n = − ϕ b n − 1 − λ b n + 1.
To proceed further, we substitute (A 3) into (A 2): ( s n + λ + ϕ ) ( f n − s b n ) = ϕ ( f n − 1 − s b n − 1 ) + λ ( f n + 1 − s b n + 1 ).