Tales about tails

Abstract

Necessary and sufficient conditions are given for a sequence { g ( n ) } \left \{ {{g^{(n)}}} \right \} to be a sequence of tails of a convergent continued fraction. Some special cases are also studied.

Composition of linear fractional transformations in terms of tail sequences

“…As an example we show in §3, that these formulas apply to continued fractions. This concept has already been introduced for another purpose, for the special case where {sn(w)} is a continued fraction generating sequence, i.e., c" = 0 and dn = 1 for all n [6]. We refer to §3 for information explaining the name "tail sequences".…”

General convergence of continued fractions

“…To do that we shall define some new concepts. In [9] Waadeland introduced the concept of right and wrong tails of a continued fraction: A sequence {g(n) }~=o' g(n l E t, satisfying With L as given in Definition 2.2(ii), we clearly get the following two corollaries to Theorem 4.5 or 4.1, which connect these theorems to Theorem 2.3. …”

On Periodic P-Continued Fraction Having Period Length One

“…Moreover, it is proved that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α, For further references on the subject, see also [3], [2] and [4].…”