Some New Families of Tasoevian- and Hurwitzian Continued Fractions

We derive closed-form expressions for several new classes of Hurwitzianand 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 Hurwitzianand 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.