In the paper, possibility of Appell hypergeometric function F4(1,2;2,2;z1,z2) approximation by a branched continued fraction special form is analysed. The correspondence constructed to F4 proved. convergence obtained in some polycircular domain two-dimensional complex space established, and numerical experiments are carried out. results calculations confirmed efficiency approximating illustrate...

We consider S-adic expansions associated with continued fraction algorithms, where an S-adic expansion corresponds to an infinite composition of substitutions. Recall that a substitution is a morphism of the free monoid. We focus in particular on the substitutions associated with regular continued fractions (Sturmian substitutions), and with Arnoux–Rauzy, Brun, and Jacobi–Perron (multidimension...

It appears that the only known representations for the Riemann zeta function ζ(z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ζ(n) for any integer n ≥ 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n ≥ 1, by using the classical Stieltjes technique. Our...

V. Berthé showed that the frequencies of factors in a Sturmian word of slope α, as well as the number of factors with a given frequency, can be expressed in terms of the continued fraction expansion of α. In this paper we describe a multi-dimensional continued fraction process associated with a class of sequences of (block) complexity kn+1 originally introduced by P. Arnoux and G. Rauzy. This v...

1. INTRODUCTION. It is well known that the continued fraction expansion of a real quadratic irrational is periodic. Here we relate the expansion for √ rs, under the assumption that rX

A systematic approach for the design of Switched Current (SI) ladder filters is described. The specifications of the filter in z-domain are used to obtain continued fraction expansions (CFE). Signal Flow Graphs (SFG) of each row of the expansion is derived and then these SFG are directly transformed into switched current structures (integrators and amplifiers). The SI blocks thus obtained are c...

Classical ways to represent a real number are by its continued fraction expansion or by its expansion in some integer base. It is commonly expected that algebraic irrational numbers behave, in many respects, like almost all numbers. For instance, their decimal expansion should contain every finite block of digits from {0, . . . , 9}. We are very far away from establishing such a strong assertio...

In a manuscript discovered in 1976 by George E. Andrews, Ramanujan states a formula for a certain continued fraction, without proof. In this paper we establish formulae for the convergents to the continued fraction, from which Ramanujan's result is easily deduced.