Shrinking the period length of quasi-periodic continued fractions (Q999714)

The author shows that every quasi-periodic simple continued fraction can be transformed into a quasi-periodic simple continued fraction having period length one. Moreover, a certain kind of quasi-periodic non-simple continued fraction is equivalent to a quasi-periodic \(N\)-continued fraction. Applications are given to \( e^{\frac 1s}, s\geq 1\), \(\frac{e+1}{3}\) and to some values of the functions \(\tanh\) and \(\tan\).