(3) (2) Pn-2 (n >= /as, as,...I SOME PROPERTIES OF CONTINUED FRACTIONS.

In this case, the continued fraction (1.6) is related to that used by Stieltjes in his study of the moment problem, and the Riccati solution U ± (x, λ) has an expansion in

All its basic results can be obtained by using the ergodic theory of random systems with complete connections (see

represents an irrational number.. Hence, large partial quotients yield good rational approximations by truncating the continued fraction expansion just before the given

Later, Hartmanis and Stearns [15] proposed to emphasize the quantitative aspect of this notion, and to take into account the number T (n) of operations needed by a (multitape)

An improvement of a result of Davenport and Roth Throughout the present Section (which can be read independently of the rest of the paper), ξ denotes an arbitrary irrational,

It is widely believed that the continued fraction expansion of every irrational algebraic number α either is eventually periodic (and we know that this is the case if and only if α is

It is widely believed that the continued fraction expansion of every irrational algebraic number α is either eventually periodic (and this is the case if, and only if, α is a

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