Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
Let \(a\equiv(a_n)^\infty_{n=1}\) be a sequence of nonzero complex-valued scalars bounded above and below, and let \(b>1\). By \(S_1(a,b)\) is denoted the continued fraction \[ S_1(a,b):=\frac{1^b a_1^2}{1+\frac{2^ba_2^2}{1+\frac {3^ba^2_3}{1+\ddots}}}\tag{1} \] This is a generalization of a continued fraction studied by Ramanujan. In the present study the authors establish sufficient conditions for the divergence of \(S_1(a,b)\) with cyclic sequences of complex parameters \(a=(a_n)^\infty_{n=1}\) of period \(c<\infty\).
scientific article; zbMATH DE number 5367288