Hurwitz and Tasoev Continued Fractions

Abstract.

The continued fractions studied by Tasoev are not widely known although their characteristics are very similar to those of Hurwitz continued fractions. Recently, the author found several general forms of Tasoev continued fractions, and by applying this method he also obtained some more general forms of Hurwitz continued fractions belonging to so called tanh-type and tan-type. In this paper, we constitute a new class of general forms of Hurwitz continued fractions of e-type. The known continued fraction expansions of e^1/a (a ≥ 1), ae^1/a and (1/a)e^1/a are included as special cases. The corresponding Tasoev continued fractions are also derived.