Acceleration of limit periodic continued fractions by the T+M transformation

摘要

We consider limit periodic continued fractions b0 + a1||1 + … + an||1 + … where limn→∞an = a is finite and not on the ray (− ∞, −14] of the negative real axis.Using related properties of continued fractions we obtain the T+m process considered by Gray and Clark, and, the process considered by W.J. Thron and H. Waadeland.It follows the possibility of choosing the best process, according to the convergence behaviour of the sequences {an}.