Chain sequence (original) (raw)

In the analytic theory of continued fractions, a chain sequence is an infinite sequence {an} of non-negative real numbers chained together with another sequence {gn} of non-negative real numbers by the equations where either (a) 0 ≤ gn < 1, or (b) 0 < gn ≤ 1. Chain sequences arise in the study of the convergence problem – both in connection with the , and also as part of the theory of positive definite continued fractions. The infinite continued fraction of Worpitzky's theorem contains a chain sequence. A closely related theorem shows that