The use of the sequence F n (z) = f n f 1 (z) in computing fixed points of continued fractions, products, and series

Abstract The basic convergence behavior of the sequence {Fn} where F1=f1 and Fn(z)=fn(Fn−1(z)) is described when each fn is analytic in a region S, S⊃fn(S), and the fixed points of {fn} converge. The sequence {Fn} is then used as a process to efficiently compute the attractive fixed points of functions defined by certain continued fractions, infinite products, and series.