Acceleration of extended Fibonacci sequences (Q1088368)

The authors discuss convergence acceleration of the sequence defined by \(C_ 0=1\), \(C_{n+1}=1+a/C_ n\), \(n=0,1,..\). where a is a nonzero complex number. Some results applying Aitken's \(\Delta^ 2\) process and Shank's transformation to this sequence are given. The rate of convergence is studied showing the superiority of Aitken's process.