(τ(p)x−p11x2)∑∞n=0τ(pn)xn=∑∞n=0τ(p)τ(pn)xn+1−∑∞n=0p11τ(pn)xn+2
=∑∞n=0τ(p)τ(pn)xn+1−∑∞n=1p11τ(pn−1)xn+1
=τ(p)x+∑∞n=1τ(p)τ(pn)xn+1−∑∞n=1p11τ(pn−1)xn+1
=τ(p)x+∑∞n=1(τ(p)τ(pn)−p11τ(pn−1))xn+1
=τ(p)x+∑∞n=1τ(pn+1)xn+1=τ(p)x+(∑∞n=−1τ(pn+1)xn+1−τ(p)x−1)
=∑∞n=0τ(pn)xn−1 olur. Buradan ∑∞n=0τ(pn)xn çözüldüğünde
∞∑n=0τ(pn)xn=11−τ(p)x+p11x2 elde edilir.