If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued fractions. We apply this theorem to two general classes of q continued fraction to show, that if G(q) is one of these continued fractions and |q| > 1, then either G(q) converges or does not converge in the general sense. We also show that if the odd and even parts of the continued fraction K∞n=1an/1 converge to different values, then limn→∞ |an| = ∞.
Journal of Computational and Applied Mathematics
Bowman, D., & McLaughlin, J. (2004). A Theorem on Divergence in the General Sense for Continued Fractions. Journal of Computational and Applied Mathematics, 172(2), 363-373. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/41