We derive closed-form expressions for several new classes of Hurwitzian- and Tasoevian continued fractions, including [0; p − 1, 1, u(a + 2nb) − 1, p − 1, 1, v(a + (2n + 1)b) − 1 ]∞ n=0, [0; c + dmn] ∞n=1 and [0; eun, fvn] ∞n=1. One of the constructions used to produce some of these continued fractions can be iterated to produce both Hurwitzian- and Tasoevian continued fractions of arbitrary long quasi-period, with arbitrarily many free parameters and whose limits can be determined as ratios of certain infinite series. We also derive expressions for arbitrarily long finite continued fractions whose partial quotients lie in arithmetic progressions.
Institute of Mathematics, Polish Academy of Sciences
McLaughlin, J. (2008). Some new Families of Tasoevian- and Hurwitzian Continued Fractions. Acta Arithmetica, 135(3), 247-268. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/52